| My general advice is: when something doesn't feel right, it probably isn't.
I think you should either give your finger some rest or see a doctor of some kind. Anyway, I don't think it's normal. I myself play a few hours a day (yesterday, for example, I had about 9 hours of rehearsing) and also am surrounded by several enthousiast musicians, but haven't experienced or haven't heared about any sore feelings or something.
Maybe should also have a look on your technique. It's possible that you're putting too much pressure on your fingers or making some other mistake of some kind that's doing harm. | 
