I have had similar problems off and on in recent years.
after seeing a doctor and getting the issue fixed (rest/prescription for inflammation in my case) I did a couple things:
1) dropped from 16 lbs to 15 lbs in my equipment
2) I wear a wrap around my wrist, this one specifically
http://www.stormbowling.com/neoprene-wrist-support-ac6713) I went to my pro-shop and before we started drilling my first 15 lbs balls, we changed spans and pitches.
for me, the change in spans/pitches probably did the most for relieving the pain and preventing it again. I am 2 years into my switch to 15 lbs and I still use the occasional 16 lbs ball and have no issues, but all the equipment I do throw has been updated to the latest span/pitches.
one thing to remember; while the SYMPTOMS might be the same for some of us, the underlying issue may not be. your best bet is to see your doctor first.