What is causing my wrist pain?

About a week ago, I was doing push ups to prepare for basic training in January when i noticed there was a pain in my right wrist every time I put weight on it. I let off for a few days, and it seems to have gotten about 50% better... but now my left wrist is hurting too. They both have a slight burn on the outside of my hand. My left hand doesn't hurt from weight, it just slightly aches and slightly burns. My right hand still hurts a little when I put my weight on it, and has the same weird burn or tingle on the top of my hand and wrist. I have full range of motion otherwise, and there are absolutely no tinder spots anywhere. I know self diagnosis is bad, but I want to know what I'm up against before I save up the money for a doctor visit. I'm seriously considering doing the SEAL program, so I need this to get better if at all possible. I'm 18, if age is a factor.