The outer side of the elbow is known as the lateral aspect. Lateral epicondylitis is a very common overuse type of problem. It shows up as pain on the lateral epicondyle or the bump on the outside of the elbow.
The pain can usually be increased by palpating the area (putting pressure on it) or by contracting the muscle that attach there. You can do this yourself - try to bend your wrist upwards (called extending the wrist) against resistance from your other hand. If the pain increases, you probably have lateral epicondylitis. Another test that is sometimes used, is the middle finger test. Here the middle finger is held straight out, while pressure is applied downward on it. This is also occasionally positive in lateral epicondylitis.
Most people know of this disorder by its common name - tennis elbow. But, most patients do not get it from playing tennis. As stated, it is usually an overuse syndrome, or from poor biomechanics.
It is treated with rest, antiinflammatory medicine (if the patient can take it), ice for acute pain (heat is more soothing though), and then a very gradual return to regular activities. Splinting the wrist sometimes helps to prevent use of the muscles that attach to the epicondyle.
Steroid injection are sometimes used, if other treatment fails. Usually, no more than three injections should be done. If all else fails, there is a surgical treatment for this. However, without a proper rehab program, the condition will return. Mainly, because the patient just falls right back into their usual poor biomechanics and overuse of the muscles. And, many patients can avoid surgery altogether by doing the proper rehab, emphasizing proper biomechanics, stretching, and gradual strengthening, tailored to the person's occupation (also called work hardening).
If the symptoms do not go away with the usual home treatments, or they get worse, you might want to see you physician about it.
Good luck.