Also be sure to check your brake lever/shifter positions, both laterally and the angle. I see a LOT (probably the substantial majority) of riders who ride with improperly positioned controls.
When you are in your typical riding position, grab the grips and place your index finger on the brake lever as if you were about to slam a panic stop. Your finger should be a) straight out from the knuckle (i.e., not angled to the side) and b) your finger, the back of your hand and your forearm should form a straight line. If there is a break in your wrist (i.e., most riders), this will impinge the ulnar and median nerves as they pass through the CT. The ergo grips definitely help with this, but even then, most riders don't have them adjusted properly. They are NOT intended as a place to rest your palms . . . they are widened to promote proper hand placement.
Many people also develop a bad habit of resting on their wrists, which is fine if your wrists are straight, but not if they are bent. Being mindful of your hand position while riding takes some practice but eventually becomes second nature.
Also, many people try the padded/gel gloves . . . which work for some, but not everyone. The problem is that the gel adds bulk to your palm which can actually worsen the problem (it does for me).
The rec above for a cold compress is also wise.