I'm not a doctor so what I tell you here I give to you completely without prejudice. Use it as you will, I hope it helps you.
For many years I studied classical guitar. This coupled with using computer all day I suffered from RSI for a very long time. I tried everything under the sun to fix it. It's now been completely gone for several years. I've also passed this information on to two other people and it worked for them too.
The first thing you need to do is see a doctor. You have to know what you're dealing with. There are many things that can go wrong so you need to make sure you're treating the right thing.
Okay, assuming its some sort of RSI, CTS, tendonitis, etc...
If you're in a lot of pain then you need to rest. You need to be careful here as you can and up resting forever! More on this later.
Forget anti-inflammatory drugs, they're not that useful. Take a look around at any sport and look at what they are doing. Think of the money involved here, think of the time and energy they've put in to finding the best solution to the problem. The answer is ice. Every night stick your hand in a bucket of ice up past the wrist and hold it in there for as long as you can. Trust me it's not nice. Pull it out when you can't stand it anymore then repeat (don't give yourself frostbite!). Do this for about 20-30 min. When I started doing this after about a week it was the first time I'd had any relief in six months.
Now for the bit you don't want to here. It's easy for this type of thing to become psychological. Don't get me wrong, you are injured, but (and you may already know what I mean) it's one of those thing where the more you think about it, the more you nurse it, the more you feed it. It's a bit like when you have a bad headache it's worse when you obsess over it. Like I said before you could rest it for every. If you don't move at all then it will feel stiff and sore.
So, the following video was the biggest change form me. I found it completely by accident. After this point everything changed and I've never had a single problem since. Not one.
EDIT: Here's the rest of the vids
http://www.youtube.com/user/ottottojazz/videos
This guy has a few videos you should watch all of them. What he's talking about completely eradicated the problem for me in a very short time. I started just like her say with a few small hand weights and moved up slowly from there.
Good luck!