Wrist pain for a few weeks?

I believe it could be tendinitis, but I'm not really sure. This pain began when I was doing my second round of Insanity, most likely during the push-up portions. There is no pain when I clinch my fist or pick normal things up during the day. The pain really only comes when I do any kind of activity where my hand goes back toward the top of my forearm (the best example I can give is doing a push-up). I plan on getting a wrist wrap that I can use for now while putting as little pressure on it as possible. I'm just curious if anyone else has gone through something similar and/or has tips for me to help heal my wrist as I will be going into the Air Force soon and obviously will be doing plenty of push-ups.