+1 here on getting on a professional bike fit. Worth the investment! I have had to cope with ongoing neck and shoulder problems from working at a computer, and have dealt with the type of pain you're talking about while riding. You'll be *amazed* at the difference that even very small tweaks can make to your riding comfort when you're in the hands of someone who knows what he/she is doing.

For example, your saddle position might be off---too high, too low, or tilted ever so slightly down in the front, causing you to slide forward and support yourself too much with your arms.

Or your reach might be wrong for you, a problem that often can be remedied (fairly) easily with the right stem length or a different handlebar. I just got a new bike a couple of months ago and my BF switched out the original stem for a significantly shorter one that doesn't require me to lean so far forward. Heaven compared to my last set-up!

Good luck, hang in there, and by all means don't give up your bike! As KnottedYet said, you'll get lots of support and advice here on TE on this subject!