Upon looking at my status in adventure mode, I see that my right hand "needs setting". Is there a way other than simply time/rest to deal with this, or do actual doctors exist?
No, you can't receive medical attention in adventure mode. You can fully regenerate by turning into a werebeast and back, which happens every full moon if you are infected by a werebeast's attacks. The next best thing to do is to wait (doing so by traveling on the world map is easiest). It is a good idea to skinny dip after getting injured to prevent infections, preferably in running or at least not stagnant water..