The treatment model is odd. Each treatment results in a changed state for the injury (possibly to the same one as before), and it seems random what you get (taken skill into account, though). This means that to get the fastest possible healing you should stop treating the injury when it's in as good a treatment state as you (think) you can get.
Shamans are presumably good at the Physician skill, which means they're likely to get better treatment results than your own character, but apart from that there's not really much point in seeking out a shaman rather than perform the treatment yourself.
There is one major exception to this: if your character has suffered major blood loss, treating the injury can open the wound up again which can be lethal if you don't have the blood staunching incantation. In that case it's best to seek out a sage (I don't think they can open up wounds, but I don't use them much), or leave the wound untreated until you've recovered enough blood to survive a wound opening mishap.
Each wound can be treated once every day (although some wounds may have several treatment stages, e.g. cleaning and dressing, both of which use a Physician roll (and potential for skill increase). The "day" uses the same rule as sacrifices, i.e. the day changes over sometime in "morning" with nothing to indicate exactly when (a day changeover may result on embers disappearing, which can give you a clue). I try to perform all "once daily" activities in late morning.