Oh dude... I would actually recommend seeing a doctor if you can. And not doing any more pushups until you have done so.

I have an lj friend with a similar-ish issue; I have asked if I can point you to her posts on it (and linked back here, so she might post herself). But her issue seems to be an overuse problem, and if doing pushups makes it worse, doing more may continue to make it worse. Especially if you have to be on a keyboard a lot, it seems very risky to me until you find out what the real problem is. The fact that incline pushups are a problem as well -- which means you're putting only some fraction of body weight on your wrists -- seems pretty worrisome to me.

With all the usual caveats that I am not a doctor, and nor do I play one on tv.