Tennis elbow is a tendon related problem, meaning simple tasks such as firmly gripping a coffee mug should be painful to a degree. Also be aware of Golfers elbow, same tendon problem but on the inside of the elbow, pianists can develop this too. Posture is a normal culprit, as it excessive tension.
Posture wise, aim to the have the balls of your elbows sitting just below the level of the white keys, and sit far enough back so when playing a c major scale, you can cross both elbows to the middle of your chest without them hitting your body.
I thought i had tennis elbow while practicing several of Chopin's Polonaises and Rach's Preludes, yet my doctor commented it was a muscle strain, not a tendon one, her exact words were "A tendon problem is immediately apparent, the simplest task will set it off"
Use Ice and Heat and alternate for a week. Fixed my muscle issue and it never came back. Also stretch a lot before playing, and although it may sound silly, constantly shake your arms at your sides to relieve any building tension.