Can i still do push ups with tennis elbow?

Yes, if not painful: Usually the result of repetitive stresses. I would position your hands in a postion that does not produce pain. You can also stretch those mucles by holding the arm straight out in front of you you and use the other than to gently bend the wrist down toward the floor to feel the stretch across the top fo the forearm mucles, hold for 30 seconds and repeat x3. Consider a brace with activity.

Possibly: Usually the pain from tennis elbow comes from when the elbow is nearly fully extended. However, any stress on the elbow can cause it to become inflamed. Thus is generally tel my patients, if it hurts -- stop, if its sore -- slow down. Listen to your body.