I am also learning button accordion and get pain in left arm and shoulder more than elbows/fingers from operating bellows. On a B/C instrument I don't actually play the chords/basses much, so can't really blame that.
At one stage I had constant "toothache" in my left arm and went to physiotherapist who tracked it down to a nerve root problem in the lower neck: with her help and some exercises, now much improved. I also play guitar, and she felt that a lot of our (musicians') problems are down to bad posture. Take a look around the next session you go to and see people hunched over their instruments, squashed into chairs that don't fit them, playing around people who are trying to get to the bar, etc!
I also play bodhran and never get RSI with that despite the repetitive action: the secret is to be RELAXED and have a good shake-out between tunes! When I was learning my forearm used to seize up and I got blisters on my middle finger from the beater: not any more.