Pain and tenderness just below and near the outside of the elbow is commonly due to inflammation of the tendon of the wrist extensor muscles in the forearm (the muscles that bend your hand backward). It is a form of extensor tendonitis.
Called "tennis elbow" because it's common in tennis players, it is an overuse or improper use syndrome. Chronic or excessive contraction of he wrist extensor muscles causes inflammation of the tendon attaching these muscles at the elbow. Every time the muscles are activated, it causes pain in the tendon and at the tendon attachment.
The wrist extensor muscles in the forearm should be massaged, then iced and rested. The inflamed tendon must be protected so it can heal; this is done by a compression band worn just below the tendonous attachment to relieve stress on the tendon.
As an ACTIVATOR Chiropractor, I find tennis elbow is associated with particular misalignments of the bones in the forearm, the ulna and radius, and often of the carpal bones in the wrist. Correcting these misalignments is an essential part of my treatment plan.