Jeff is right, you are probably gripping the bars too tightly. Even though that is the throttle side, you barely have to hold on at all to keep it where it should be.
If you relax your grip, and there is still pain make sure that you are not using your arms to keep you up, on sport bikes this compresses the wrists, causing pain, on cruisers this can over-extend the wrists, causing pain. It is best to use your core (abs & back muscles) to keep you upright. I don’t think this is the case since it is just your right wrist that hurts, but something to keep in mind.
If all else fails, look at getting a Cramp-Buster, I’ve heard varying reviews on how well they work, but they all say it works.
Enjoy the ride