There is no divine, natural, bardic, arcane or any other kind of magic that can do anything remotely as useful. There is no alchemy, no science, no a way of a mind that can do anything remotely as useful. No ancient relics, no alien knowledge, no outerwordly artefacts are going to work either, even if they look like they might. The natural healing is a slow, painful and not a very optimistic process in a world which is centuries short of the discovery why hand washing is good.
As a healer, you mostly kills humans, elves, dwarves, wizards and any kind of souled beings – 'inner light' is really just a soul, a desensitized euphemism for. Demons, angels and other outerworldly denizens won't do, monsters mostly won't do regardless of their power (with the exception of golems) and rare souled beasts (such as wild whales, ravens and wolves) are either extinct or on the verge of extinction, being hunted at mass for their precious essence. Depending on that world creator(s)'s view of orcs and other non-pretty sentient species, they can share the same fate.
Needless to say, in this world both a capital punishment and a black alley murder are slightly more common, euthanasia is more accepted and suicide is only frowned upon when it is done alone, with no healer around. After all, why let a criminal waste their years in life sentence if they can be used to heal their victim's family from something nasty? There is the whole gray market of souls, of course, and black market and white market, and, if your world is sufficiently advanced, souls might be easier to come by using farms to breed and harvest ravens, wolves, orcs or humans.
As a healer, you might not enjoy the process of the killing itself although many of your colleagues would disagree. No worries: your teammates can help with this, as long as a killing is done in your close presence, you know who is dying and you are able to quickly take the 'inner light' out of just killed body (denying it any afterlife, btw) and store in a glass flask, a mirror ball, a jewel, or maybe even an eye of the crystal plague victim if you so wish. Jewels are the best not only because they are small, durable and become very pretty, shining, very valuable gems, but because the inner structure of properly precious stone makes the escape of the soul almost impossible, although a mirror ball (where the soul is lost in own reflections and cannot find an afterlife) or a glass flask with peculiarly twisted neck work just the same.
With stored souls in your disposal you can knit multiple fractured bones and make four-degrees burns from wizard's fireball heal in the instant. You can heal diseases, both acquired and inborn, poisons, loss of senses and memories, drug additions, madness of any kind, stress, infertility and ugliness. You can break curses and involuntary transformations (and even heal the victims of crystal plague), bring dead back to life as if they never have died and even fight the ageing (including your very own), healing the time and death themselves. Many, many good things can be done with such inner light for good people or for any other people with good money.
You don't even have to worry about the competition from demons, angels, gods or those pesky wizards, as demon, angel and divine healing always turns people into noticeably something else, while wizards aren't able to duplicate your specific inborn gift even close, and won't ever be able to, however they try. You and your colleagues with the same gift are the only sources of consequence-free, fast, powerful, clean, predictable, absolutely effective and stable healing in the world.
Being momentarily engulfed by another soul is quite harmoniously euphoric experience to you, there is nothing painful in it: even the soul of sadistic mass murderer of children is a warm ember of happiness. And, to think about it, by dispersing said killer's soul into nothingness during the healing, you surely create a better future for it than the eternity of suffering in some faraway hell. For many healers to heal is a reward by itself. Best of all, as the soul is a mostly mindless thing (made of all joy, warmth and happiness that the person even had a potential to experience), you don't even have troublesome flashbacks of somebody's else lives, neither their memories, nor hopes, nor worries.
And in very rare cases when such things happen, and the burden of endless killings starts to weight upon your own precious soul – hey, you can heal this too.
Could be a class. In this case use middle road progressions (rogue or inquisitor in PF, specialist in ODnD, warlock in 5E) for basic attacks, HP and saves (con/wis saves probably the most fitting). By itself the class is rather limited in what they do - its only purpose is to collect souls, heal with them, and maybe to know how close somebody in vicinity is to being collected and if they have a soul or no. It is the best fit for not a very complicated system or used as a special module-talent in more complicated ones.
World-wise it is probably the most playable in a world where most of your opponents are humans or something equally as renewable souled resource. The vast majority of monsters aren't profitable in this respect. Also keep in mind that most of non-adventurer NPCs have very few HPs and easily healed with 1st level spell, making the healer NPC in demand and wealthy.
No other class or race has the access for the same level of fast, effective, stable, predictable, consequence-free healing so you might want to power up healing spells a bit numerically.
Mages/bards/driuds can speed up the natural healing but it still going to take hours at best (days more commonly) and their powers cannot deal with many illnesses and ageing, although they can sterilize the wound and eliminate some common consequences. Psionic/monk healing eats into their lifespan and abilities (by stressfully speeding up the natural regeneration) and they only can heal themselves. Demon/fey/divine/angel healing, while available freely, should be treated as a mutation and/or a geas and/or possession stage for every healing effect provided, subtle at first. If not treated by an actual healer an outsider's help will eventually turn a character into one of demons/fey/divine servants/angels: the healing those creatures provide is to sugar-coat the way those species propagate in this kind of universe. Kind of like a parasitoidal wasps injecting some cocaine before laying an egg or applying a band-aid after to mask an effect.
There are no spell-slots to use, as the healing is tied entirely to the inventory and amount of actual souls the healer was able to collect during their adventures (or buy from a market in a world with farms). Barring killing sprees, DM has more control over how much of healing is available by setting up enemies, with souls or without. No memorization: all healer's ability are innate. Casting is mental, takes a standard action and there are no somatic or verbal components. The healer might be capped on the level of a soul they are able to collect (say, equal to their level, so stronger souls than that cannot be caught) or, more traditionally, on a level of healing effect they are able to cast (say, level of spell x2 - 1, so fifth level healing effects are available at level 9 of the healer). Using a stronger soul on a weaker spell-effect is either wasted or boosts the effect, at DM's preference.
My default is 1 level (CR, HD, however the power level is counted) of slain souled creature for the 1st level of healing spell-equivalent. +2 more of the same (to total of three) for second level healing spell-equivalent, +3 more (total six) on third level spell, +4 more (total of 10) for four, etc.
I use Pathfinder spell levels as a reference for healing effects because PF has a ton of spells. So Cure Critical Wounds is a forth level spell, Heal is sixth, etc. Lesser restoration is an equivalent of cure infertility. The healer is able to make people younger (cure ageing) as a fourth level power in a rate of about 5-10% of max lifespan per spell, and push the limit of life (adding to a maximum life limit) as a eight level spell in ratio of 10% of max lifespan of recipient species per cast (ten casts is +100% more lifespan, so human is going to live up to 200 years).
If convenient powerful healing should be more rare but lesser one still common, the additive Fibonacci sequence ( 1, +2 (3), +3 (6), +5 (11), +8 (19)...) can be set, the difference go up drastically for higher-level healing. But any sequence can be used, really, even logarithmic for extreme non-usability. Use non-additive sequences (level of spell cast = amount of levels (CR/HD) of soul, for example) to ease the cost.
Storing souls in peculiar items that at least 1 gp worth per HD/level/CR of the creature (it can be more pompous if you so wish), such as bottles with twisted necks, mirror balls, gems and such; those items are reusable. To simplify the inventory, you can use a pool of gold value of such items and not separate objects; just note how much of the pool is currently tied up in collected souls and what levels are those.
To collect the soul the healer should be within close range and able to know where the dying person is with precision of about 5 feet (see or sense in some way, pinpoint a square if the dying creature is invisible, etc). Thick walls probably won't be a problem. The collecting should be done as a standard action within 1 round/level of the healer since death, otherwise the soul goes on its own merry way.
I have very strong Athar sympathies and, as it chafes me that gods pretty much usurp the best healing in DnD and make it entirely consequence-free to cement the deal, I like to come with alternatives nobody going to use in an actual game (my favourite fast solution is to ban all kinds of clerics and paladins, give full healing to bards and/or druids and just use the binder class as the only way to contact the divine). Here the healer operates on the same principle as a gods do in standard ADnD universe, but without unlimited access to energy of a plane (into which all souls of divine worshippers eventually melt) healers have to salvage. It can only be playable in a setting were no normal magical healing exists, because otherwise everybody would just play standard healing classes anyway.