I had really bad RSI for two years. I couldn't use keyboard or mouse because they hurt too much. I had to use a graphics tablet as a mouse, and programs like Dasher as a keyboard. (When I Rule The World was written almost entirely in Dasher...) It was a real pain (in more ways than one), so take care of yourself!
Specifically, POSTURE and BREAKS are the two biggest things to watch. Take a break every hour or two, for two to five minutes. (It's a pain, I know, but it's one of the most important things.) Rest your hands during that time; there are a number of stretches you can do which might be useful.
RSIGuard will show you many of them.
Posture is the other thing: try to avoid slouching (this is really hard I know), sit in a straight-backed chair, use a wrist rest at the computer, and try to avoid bending your wrists to unnatural angles.
I really, really recommend taking this seriously and taking care of your body earlier rather than later, because it takes a long time to heal, and longer if you leave this unaddressed for longer. (I'm still not fully healed - I have to use wrist braces whenever I'm at a computer.)
And yeah, a physiotherapist can give you some wrist braces or some more specific advice.