Danb,
Unless you've been on a high-protein, high-fat diet, I seriously doubt that gout is the problem. You may have some tendonitus, and this could be caused by improper position of the hands in relation to the keyboard, and especially, your computer's mouse. If at all possible, position your mouse on a mousepad that is situated at a height that allows you to keep your wrist as straight as possible and your elbow to forearm position bent at 90 degrees. The same holds true for playing the keyboard. This takes a lot of strain off the joints and tendons, thereby decreasing any possibility of excessive strain and inflamation. Over the counter anti-inflamitory medications, such as asparin will also help reduce the inflamation and aleviate the pain. When using the computer's mouse for extended periods, I would stongly suggest using a wrist brace, one that prevents wrist movements in all directions.
Hope this is of some help,
Gary
(The doctor is now on vacation!)
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