+1 what Knott said. This sounds like ulnar nerve compression. You need to move around on the bars as mentioned, get your bike fit... also mentioned and get some gloves with good padding over the heel of the hand on the pinky side.

The bike fit is probably the thing that will make the most difference. You need to be in a place where you can sit on your bike and "piano key" the handle bars. The most common correction for too much weight on the hands is bringing the seat up a little and sometimes back a little. But it is really best to have someone take a look at you and figure it out because it could be a host of things.