If you are riding a sport bike, be sure to use your legs to help keep your body posture. Leaning to heavily on your wrists is going to cause discomfort. Also being new to riding, you do develop a bit more muscles to help stabilize yourself. Try and think of any other time in your normal life that you are holding into a bar for hours at a time. Make sure when you just start out to try and keep your rides shorter. Don’t try and get the iron butt award right when you first start!
Looking now at your profile pic I’m assuming you actually ride a cruiser (I’m guessing maybe a Honda Magna 500 or maybe a Suzuki Boulevard s40??? Too small of a pic to tell). So the sport bike advice isn’t going to help you, but maybe someone else will find it useful. So my best guess is that it is a combo of 2 factors. One, you unconsciously have a death grip on the throttle and are holding your wrist tightly in a bent position. Secondly, the vibration is numbing your hand and helping to make it more sore. You want to be loose enough while riding to be able to swing your elbows like you were doing the funky chicken at any time. When you are new to riding it happens all the time that you are holding on way too tight from nerves. For a while you will have to consciously remind yourself to loosen up. Slowly but surely it’ll get more comfortable.