This is an old question, but I suffer from wrist problems (and have for probably 10 years now) so I feel like I should share my experiences.
The first thing I want to say is - if you are experiencing pain, go and talk to a doctor. Keep talking to doctors until someone acknowledges that wrist pain is a serious condition and they take you seriously. This kind of pain does NOT go away, and it will NOT get better without work on your part.
I never found the recommended exercises did much for the pain. These are the things I found worked best:
- Try to work/play in an ergonomic environment - Some companies I worked for offered ergonomic consultants to come and take a look at my work environment, and the tricks they taught me I took home to customize my home rig. There's sort of a "standard ergonomic/posture" diagram, this one looks about right. The part I found the hardest was trying to adjust the height of the table and the chair to match. Most tables are fixed-height, and even adjustable chairs have a range. If your feet are up off the floor when you get the desk/chair adjusted right, get a foot rest.
- Try different mice. There are many that are billed as 'ergonomic' including trackballs, and some change the position of your hand to something you might find more comfortable. I found that the Logitech style (ie, MX518, although they make many with this shape) works best for me.
- Use a brace. I found that one with a splint that goes about 6" from my wrist towards my elbow worked best. My doctor suggested I wear it while I sleep, because some people (especially those who use computers all day) tend to 'type in their sleep!'
- Pick your battles. Sometimes I will opt not to continue playing a game because it is just too reliant on button mashing. I'd rather make it to retirement and be able to enjoy myself than burn out on a game now.
When I have pain, I like to pick up a small weight (ie, 5 lbs) and lay on my back. I rotate my wrist in different ways, similar to the exercises that people have mentioned. I also find that using a 'stress ball' (like this one) can help to work the joint and get it moving properly.
I've been in physical therapy before, and the therapist told me a few things that I find helpful to remember. One is that you should try to exercise every day. When you forget or get complacent, the pain will return. Even 2 weeks without a proper exercise regimen can cause issues to return. The second thing I learned was: if the exercises seem inconvenient or are a pain in the butt, remember that your choices are either pain on your schedule or pain on pain's schedule.