Stretch your arm in front, palm upward. Make a fist and relax. Try to make a fist again, but with the opposite hand applying resistance (pressure) to prevent you from doing so. If this causes pain or discomfort at the inner (medial) elbow, that's bicycler's (or golfer's) elbow.
Now stretch hand with palm downward. Raise hand up against pressure from the opposite hand. If there is pain or discomfort at the outer (lateral) elbow, that's tennis elbow.