If you were a stressed civil servant I would suggest that you have RSI and should take the next 6 months sick leave and of course claim many thousands of pounds in compensation.LOL
If you are not and this is a fairly recent occurrence then it might well be be a combination of things. I noticed that when I was in full cancer treatment mode I too had problems with my right hand that got worse after using the mouse for a while, As I am an ardent gamer this was difficult to avoid.The fingers on my left hand did not fare any better, no doubt pressing the WASD keys whilst gaming was the cause. Oddly I did not notice any problems whilst gaming but it was mighty painful when I stopped.
I started to use the Nurofen gel which I rubbed into my hands and wrists for a while. I don't seem to have any problems these days.
Maybe a track-ball might help you? I couldn't get used to it but there again I cannot use a track-pad either.