Sorry to hear that, Oli,
I agree with Daniel, it sounds very much like a case of carpal tunnel problems, and you're quite right, it won't go away unless you take some action.
First thing, if you haven't already, is to get to your GP. If it's hurting all the time, then the movements of the joint during daily life are probably not giving things a chance to heal - I had to wear a wrist brace for quite a while when I got it bad, and stop playing my beloved bass guitar etc., but my wrists sure seemed glad of the rest even after just a day or two.
From what I was told at the time, the problem is not so much with moving the mouse, but due to having the thumb and pinky/ring finger constantly locked in the same position to grasp the thing - the force required may be very small, but our joints are designed for movement, and just don't like being jammed in the same position for too long!
I've had a much better time since I started using a track ball rather than a mouse for much of my PC work. I'll refrain from plugging any particular model, as it will depend very much what you can get comfortable with. But I would recommend something that you can sit on your lap, rather than with your arm laid on the desk top, so that you have a choice of postures.
A track ball is also more "brace friendly" too, so I found it easier to still be productive even when I needed the extra support - and while the 'track ball on lap' posture slows things down a bit, I always felt that the extra movement needed to reach to the keyboard seemed to help keeping the joints nice and 'oiled'. Having a mouse too, will still be very handy, and do take care that any track-ball can emulate middle mouse and wheel actions, otherwise you'll be cursing when you want to orbit your models!
Long term, it's just a matter of awareness - some simple exercises, and knowing the tell-tale signs that a rest or change of posture is needed have managed to keep the worst at bay for many years for me. I've only needed the brace again to wear during "down-time" when I know I've been overdoing it a bit - tucking my wrist up nice and cosy in bed so it's rested for the next day, so to speak.
All the best,
Trog.