It also might help, if you really cannot take a total break from the computer, to at least make sure and step away from it for short periods of time throughout the day. Pause everything, go have refreshment or a walk around the block.
Any repetitive motion can lead to similar problems. People who use the computer a lot, people who stand at cash registers and scan purchases even have a problem. These are acknowledged work related injuries and the sooner you get a diagnosis and treatment the better your prognosis is for a cure. Nothing at all to feel shy about.. this type of thing has ended lots of careers.
If you don't feel comfortable talking to your doc about this you might talk to a doc who treats sports injuries, or even a rheumatologist on the off chance it is some kind of arthritis. These people would recognize a problem with a joint, even if it isn't their specialty.