I have this symptom from Lyme's disease
If it is affecting both sides it could be hyperventilating. You don't have to be breathing fast to have hyperventilating symptoms. You could be breathing shallow and taking gasping type respirations. Sometime it gets so bad that your hands kinda freeze up into a claw like position and will hurt as you oxygen and CO2 stabilize. I am not saying this is what it is for sure but I have seen it many times in the ER. If you are really concerned you should see your doctor.
Not sur what causes it but I have found something that helps it go away faster within about 10 Min's to a half hour. Just make sure you always have so germ-x of some kind of hand sanitizer with you. And plenty of paper towels. Pour a lot on your hands and rub them together until you feel dirt or grime of some sort start to come off if feels like grit between your palms. Wipe off with a towel do it a few more times and your hands will start to feel a lot better.