In addition to the other good advice here, I'd suggest having your teacher watch you with an eye to any aspects of your technique that might be causing injury. Also, while it's very possible that something about your piano playing caused this, don't eliminate the possibility that some other source of injury is responsible. I once had a really painful right hand and was worried about what I had done at the piano to mess it up so badly. My teacher watched me play and said she really couldn't find anything tense or harmful in my technique and stated asking questions about what else I'd been doing. It turned out that I'd recently stacked about 4 cords (a few tons) of firewood grabbing the logs end on, one by one in my right hand, and hadn't noticed any pain right away, indeed hadn't noticed it until I started playing the piano. A few weeks of working on pieces for the left hand alone and I was good as new.
I had a lesson and this is exactly what happened. There doesn't seem to be anything wrong with my technique. I'm at a loss as to what could possible be causing it though. I'm going to try readjusting myself while practicing just to see if it helps. I think its from practicing at full force (like what one of the comments said above). I also thought about it, and it's more of a muscle pressure pain than tennis elbow (considering tennis elbow is a tendon related injury)