Wrist

Sounds like too much of your weight is being put on your wrist or your wrist is an awkward position. If so, in either case, it's possibly an issue of bike fit. There are so many things you can adjust on a drop bar bike to get more comfortable that it's hard to list them all.

On a drop bar bike when I'm feeling too much weight on my hands, first thing I try is to loosen the handlebar stem clamp and then raise the bars, slightly, for an easier reach to the hoods. Can't go too far, here, because you don't want the drop section of the bars at too much of an angle or you could lose your grip when you ride in that position.

Another option to take weight off the hands is to move the seat a bit forward or in extreme cases, just go to a shorter handlebar stem.

Another issue I've had on men's drop bar bikes is too wide a handlebar, since I have to go to the larger sizes on a road bike because of my long inseam.

Anyway, it would be well worth your time to take the bike to your local bike shop and visit with them on fit or get their suggestions as to the source of the problem. Sure beats messing around adjusting parts positions, back and forth, on your own. That can sometimes even make things, worse.