Is your pain coming from another cause or is it only when you ride?

If you have diagnosed carpal tunnel you may want to try some exercises to reduce the symptoms. Lots of info on the interwebs on that.

If you are feeling hand pain only when you ride there could be a number of factors at play...

-saddle height/pitch
-Bar width/sweep
-grips
-lever position
-Death gripping the bars

I had to train myself not to death grip the handle bars. Its hard not to do.,I also do hand and forearm strength exercises to reduce arm pump.

Good luck and I hope it gets better. Sore hands really make riding terrible.