Position is important, and since you've had your bike fitted (did it take at least an hour??), then I'll assume that's not the problem.

Core strength is a big factor in position. If your core cannot hold your body up properly, you'll end up putting alot of weight on your arms, hands, and shoulders.

I've found the best thing to improve my core strength has been Pilates. Just make sure you go to a well-trained instructor, not some pseudo-pilates taught at some gyms (you can get injured in those classes--Body This and Body That).

Hope you get some relief soon!