RSI shouldn't be an issue at the piano if you use your body the way it was designed to be used. And how is that? I'm glad you asked.
Though it's not possible to diagnose your specific problem without looking at you play, here are some things to watch for. Make sure that your hand and arm are a unit, that is, a straight line like a tennis racket, but not rigid like a tennis racket. As long as you are straight with yourself, you can be at any angle with the keyboard. This is important to know so that you don't twist at the wrist in order to avoid the black keys.
Take care not to do anything to an extreme, I.e., stretch your hand too wide, lift your fingers up and away from the hand. (The only reason to come up is so that the finger can go down; make sure that you are not holding your fingers up.)
Finally, and this is a difficult concept to describe (but easy to show and feel), make sure your arm is behind the finger that is playing. This is accomplished through forearm rotation, our most useful and efficient underlying tool. Without forearm rotation, it is not possible to even get the hand on the keys, so you already are doing it. The question is, how are you continuing to move? Ask your teacher about this.
It shouldn't hurt to play the piano. How can we make music if we're enduing something?
Best wishes for a speedy recovery.
