Magic is complicated and difficult. The human body is complicated and difficult.
Put them together, and becoming a true master is like getting PhD doctorates in two vastly different fields. While there may be many little magics that tread in healing waters, like Elaine's handling of minor injuries, healing serious or mortal injuries with magic would take not only a surgeon's skill to know what to effect and when, but also a master wizard's skill to put those energies to work in exactly the right amount at exactly the right time.
Building things has always been harder than blowing them up. Magic still has to work in the real world with real physics (at least in The Dresden Files), or in this case in real body parts inside real bodies. It's not as simple as sealing skin; diagnosing injury is an entire field to itself, let alone the treatment. Telling a body to just "grow back" without proper guidance and knowledge behind it is probably a good way to create a cancer spell, presuming a prompt outgrowth of tissue just doesn't kill the patient.
It's also treading grey areas that tend to invoke grey cloaks. Working spells on other people's flesh can invoke Second Law warnings (thou shalt not transform others). It doesn't matter if you didn't mean it; if you didn't do it right, you fail. If you screw up badly enough, bam, you've killed someone with magic, First Law violation equals swift and certain execution. So the Council is really the only resource you could study under safely (presuming you can find a master who knows the field), and they aren't the most open bunch.
Injun Joe is probably the foremost healer mentioned in the series, and it's mentioned that he goes back to modern university every now and then just to keep his medical skills sharp.
I pondered that the Wardens might know some magic in this vein, but given their penchant for destructive magic and that they need to be efficient, modern military field medicine techniques probably serve them far better.