Harry Dresden seems always to be nursing a fresh injury. Doesn’t he know any healing magic?
Healing magic is very limited in the Dresden universe. The few healers that exist actually have medical degrees and hands-on surgical experience - and even then, magic can only augment modern medicine, not replace it. Wizards mostly rely on their own natural healing abilities, which are amplified beyond normal human levels as a side effect of magic use, and even those are slow-working. Harry burned his hand to a crisp in one volume; a normal human would never have recovered, but after extensive surgery, physical therapy and time, it was almost completely healed three books later.
As Harry himself says, destroying is much, much easier than healing.
Repeated injuries and beatings are a hallmark of potboiler detective stories. You can’t have one half of a hybrid character neutralizing the other half.
The only wizard I remember who had any real skill in healing was Joseph Listens-To-Wind. He offered to teach Molly Carpenter about healing magic at one point I think. But it’s an extremely rare skill.
As you say, wizards have a natural ability to eventually heal completely from almost any non-fatal injury given enough time. Waldo Butters was the one who explained to Harry how ridiculous that was.
I believe some powerful non-human entities like powerful beings from Faerie can also heal magically but not for free, of course.
For instance, Harry broke his spine in Changes, and Mab fixed it (or at least got it working again) in return for him becoming her Winter Knight.
Exactly. Faerie medical bills are pretty nasty!
There’s a quote in one of the books that actually says that modern nonmagical medicine is nearly as good as what the best wizardly healers (who also study nonmagical medicine) can do.
He’s got Butters too, to some extent considering Butters doesn’t like living patients
Maybe a shapeshifter thing? Listens-to-Wind is exceptionally skilled in shape-shifting. Will and the Alphas have also developed rapid self-healing abilities over the year (explicitly described in Twelve Months). Goodman Grey (half human shapeshifter) also heals quickly.
Possibly Listens-to-Wind extended that capability so that he can affect healing in others
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The Winter Knight’s mantle allows his spine to continue to function. One the mantle lifted briefly and Harry was paralyzed again. Interesting to see how Butcher addresses that if he ever lets Harry escape from Mab’s clutches.
Quick & easy solution (but not necessarily the best narrative one): his magical healing factor finally healed his spine.
I seem to remember that when he broke it it was discussed that it would eventually heal on its own, but he needed it somewhat urgently…
Butcher set that up, with a daughter out of no-where.
I am not sure how most people would react if told they had a kid they did not know about years ago. I do not think most would go all Dresden over it.
It’s been ages since I read the books (I think I was still in College - I forget what the latest one I read was, maybe Skin Games? Doesn’t look like there’s been that many since…) but some of the nonhuman magic users can do some incredible healing feats, can’t day? Like, basically just short of ressurecting the dead? I think there was a fae with a knight she brought back from near death?
Ok this is probably what I was thinking of. Again I only vaguely remember this, but IIRC it wasn’t just that she healed him in exchange for becoming her knight, she couldn’t heal him to that extent unless she had the kind of power over and connection to him that comes with being her Knight? But I could be misremembering.
All wizards are human, so non-human magic users don’t count, and as I said later in my post:
But yeah, the best wizard healers aren’t much better than doctors. So Harry is best off just going to a hospital if he has a wound that isn’t going to raise too many legal questions.
I can certainly see the argument that fae aren’t wizards, but aren’t some vampires accomplished magic users in ways that don’t drive from inherent vampiric powers?
A wizard is literally a member of the White Council. Anyone else is a different kind of magic user; sorcerer, warlock, magical specialist of some kind, etc.
In the Dresden Files universe, that term is reserved as a title rather than a description, like “Doctor”, and wizards represent the top tier of human magic training and power. (You will see it used as a title sometimes like “Wizard Dresden”.)
ETA: Its possible that there is some form of non-wizard human magic user who specializes in healing and is better than a wizard at it, but I’m not aware of them being mentioned, and if they exist somehow they’re unknown to the wizards of the story or they’re kept as a secret from Harry.
Ah, fair enough. I really do need to give the series a reread.
I’ve read it more than once and really enjoyed the subsequent readings, I hope you do too. 
Harry avoids hospitals to avoid blowing out medical equipment. For example, when Michael is shot up by the Denarians he stays in the waiting area but won’t go back to the ICU when Michael is out of surgery. Many similar references throughout the series.
What the fae can do is a concept that’s much more closely tied up with what they may do, than is the case for humans. It’s the same sort of deal as them being unable to lie.
The White Council would like all wizards to be members, but they don’t quite have a monopoly. Ivy, for instance, is a wizard, but is not a member of the White Council. A warlock is not defined as a non-Council human magic-user; it’s a human magic-user who’s broken one or more of the Laws. Most untrained human magic-users end up breaking the Laws by accident, but it’s not inevitable (especially not if someone like Harry unofficially takes them under their wing).
Sorcerers, meanwhile, are by definition nonhuman. Most of the higher-powered fey, for instance, are sorcerers. It’s unclear how similar their powers are to those of wizards: Molly, for instance, still uses magic in basically the same ways that Harry taught her, (so, like a wizard) but when she does it, it doesn’t screw up the cell phone that she’s texting on (so, unlike a wizard).
Ivy is The Archive, and is never described as a wizard.
The only example I know of for a “wizard” not in the White Council is Elaine. She calls herself one (advertises in the phone book just like Harry) but Carlos says she shouldn’t do that because she isn’t one. So I guess it’s debatable if a wizard has to be in the White Council or not.
That is correct, which is why “warlock” was just one example I gave of types of non-wizard magic users. I never said that all non-wizard magical humans are warlocks. Morgan would have been really busy if that was true!
That is incorrect. In the Book Blood Rites, Harry talks about sorcerers being capable magic-users who haven’t reached the ranks of wizards. Here are some quotes.
“Kind of an industry term,” I said. “Plenty of people can do a little magic. Small-time stuff. But sometimes the small-timers practice up, or tap into some kind of power source and get enough ability to be dangerous. A sorcerer is someone who can do some serious violence with magic.”
“Like the Shadowman,” Murphy said. “Or Kravos.”
Leonid Kravos and Victor Sells (the Shadowman) were human.
Harry might agree with you though about wizards not needing to be in the White Council; he considers it more of a level of skill than a title.
“Wizard means that you can do sorcery if you need to,” I said, “but it also means you can do a lot of other things too. A wizard’s power isn’t limited to blowing things up, or calling up demons. A good wizard can adapt his magic in almost any way he can imagine. Which is the problem.”
Though I don’t recall him explicitly calling anyone outside of the White Council a wizard either.
A lot of my knowledge about these definitions also come from the tabletop RPG published by Evil Hat, which was created with Jim Butcher’s aid and vetted by him.