Its called ulnar nerve impingement.. thats the nerve that goes through your elbow and down to your wrist and fingers. If you are putting pressure on the base of your palm for a while, it will act up. Your riding position doesn't seem to be a big problem. Perhaps a shorter stem and riser bar. Make sure your brake levers angle down so you aren't bending your wrists up to grab them.
Get some good soft grips like these:
http://www.extremesteering.com/Silic..._Absorbing.htm
I have a pair and they are awesome. I didn't really find the gel gloves to help much eaither.