I agree with LtS, you probably need to use a bigger drum, also try holding the beater so that it rests on the inside of the first joints of your fingers and is held in place by your thumb opposing the middle finger not the first. (you might want to get a slightly longer beater for this) this grip can be loose but you won't drop the beater. Every couple of tunes stop and shake out your whole arm and raise and drop your shoulders a few times to break the muscle tension.

If the discomfort persists then you probably do have an RSI and should seek medical advice.