Why do I have pain in my arms?

Could be R.S.I..

If it’s a nerve compression problem, you might get similar symptoms (usually with numbness). In your right arm, I’d guess it might have to do with the ulnar nerve since it runs exactly where you specified.

On your left wrist, if it’s the same side of your palm, then it’s the median nerve, and this is a common complaint of computer typists. (read about Carpal Tunnel Syndrome)

I personally had both these kinds of pain in both arms, especially in vacations when I spend ridiculous amounts of time typing or gaming. As @rebbel mentioned, this is most probably a form of repetitive strain injury, so you need to follow a more ergonomic approach. Try adjusting the chair and desk so that you’re in the proper ergonomic position, and get frequent breaks to relax your arms and move around.

If pain persists and increases, you should consult a doctor.