This may be a classic sign of lateral elbow instability after dislocation. The lateral collateral ligament (LCL) may be torn. Without this ligament, the elbow may be partially dislocating (called subluxation). Pushing down on a stationary object like the arm of a chair actually reduces the joint (puts it back in place).
Most patients with this symptom also report feeling as if the elbow might come out of joint. There's often tenderness along the outside of the elbow. Full motion is present but turning the hand in the palm up position with the elbow extended gives the feeling that it may dislocate again.
It may be best to see an orthopedic surgeon for an evaluation. You may be able to participate in a rehab program to help strengthen and restabilize the elbow. It depends on how severely damaged the soft tissues are and what's your activity level.