You may be describing some signs of nerve involvement. Are your symptoms better, same, or worse when you bend your head toward the side of the elbow symptoms? Symptoms such as you described suggest tension on the nerve. This is especially true if your symptoms are better or go away when you bend toward the side of the tennis elbow.
Stretching usually helps tight muscles lengthen and relax. In your case you may need to stretch the nerve as it goes from the neck down the arm and into the hand. This can be done but you'll probably need a physical therapist to help you learn how.
If your symptoms aren't better after just a few sessions of nerve gliding and stretching, you may need some nerve testing to find out where the problem is coming from. You'll need to see a medical doctor for this kind of testing.