Go to the doctor. Also, don't take more than 1000 mg per day, or take it for more than ten days. If you get a stomach bleed, it will make you forget all about your hands.
1. It would really worry me if a doctor told me to take that much ibuprofen with no indication of when to stop. Hello, liver damage!2. I haven't had any problems with it myself, but I know some people who have. If it is CTS or other compression of the median nerve, you may end up just wearing a splint for a while. Some things I do to help prevent it are taking breaks every once in a while, making a tight fist for a couple seconds, then spreading my fingers out as much as possible for a few seconds, and repeating that about ten times. Do that about every half hour you've been typing and see if it helps.
Consider a ergonomic (split) keyboard.
I also bought a wrist guard/band thingie.