Tennis elbow is not always due to inflammation. Pain that first strikes the outside bump of the elbow (the lateral epicondyle) is likely due to inflammation. However, symptoms that are chronic and unchanged after taking anti-inflammatory medications may not be tendonitis.
Conditions that involve inflammation are indicated by "-itis" on the end of the word. For example, inflammation in a tendon is called tendonitis. When tennis elbow is from inflammation around the lateral epicondyle, the medical term is lateral epicondylitis.
Rather than a problem with inflammation, you may have symptoms of tendinosis. This is a condition where the body keeps trying to repair the injured tendon. About the time healing gets underway, the tendon becomes strained again. Eventually, the body stops trying to heal the area and instead replaces normal tissue with scar tissue. This leads to degeneration where the forearm extensor tendons attach to the lateral epicondyle. Treatment generally takes longer when the problem involves tendinosis. Talk to your doctor and physical therapist to see what other treatment options can help your condition.