I had it too. In my case I think the problem is the reduced range of motion combined with abuse due to too much hand stands, rings and other stuff.
I try to avoid the positions that cause me pain: when doing push ups I use push up handles, in handstand I turn the wrists a little outwards, in yoga I sometimes used a closed fist instead of the open hand.
I also started doing stretching.
After a while the pain reduced a lot and at the moment everything seems fine, though I continue avoiding the positions that were giving me problems.
Hope this helps