I'm sure there are diseases that cannot be cured by alchemy of magicka, what about a concussion, or headaches? What about effects that http://en.wikipedia.org/wiki/Trepanation supposedly cured?

Magic and its associated alchemy seem like they are far more effective with a lot less work than real medicine is. Considering what is available "practical" medicine probably will be very slow in arriving in Tamriel, if it ever arrives at all. Based on that description in that necromancy book that was posted it seems the potential and desire is there. In fact, early alchemy helped lead to what we now know as chemistry. I guess it all depends on what Tamriel is at its core. Are diseases actual little microbes or bacteria, microscopic organisms or are they just magickal essence or something?

Magic is complicated, and healer is also very complex. Anybody read Wheel of Time? Doctors and Herbalists exist, and they do their share of work. But lets say you are infected, the first to help you is likely a herbalist. Unless you live close to the temple, etc. The herbalist servers two purposes:
*Keeping the patient alive
*Curing the patient

If you got a flu(atleast the norwegian weak version), a healer will only do someting if it bothers to. If you are ill however, its a different story. If you are ill, why sit in days in bed with herbs and medicine when the healer are capabel of curing you in 5 minutes? It is a dam good question. In most cases, the healer will happen before the doctors and herbalists. Simply because there is quite a few healers that is spread around the country.
In Wheel of Time, the Aes Sedai is either hiding, doing intriges, in the White tower, tracking down shadowspawn, killing each other, or lack the ability to heal. And very few trust Aes Sedai, they are way to manipulativ and powerfull. They even got their own spot in their folklore as being as corrupt and evil as the shadowspawn, alot of people fear them.

In Tamerial it is kind of different, the healers are spread out trough every minor city mostly. And the healers are not feared at all.

We should still probably keep in mind that this is a altered universe, there might and there might not be so to say.

There might be doctors as well as healers and what else but there still might not be doctors, but we know that healers exists.