A great portion of elbow issues are due to problems upstream at the shoulder or scapula (shoulder blade). This can be weakness / instability or just poor movement patterns with the shoulder or scapula. Wrapping the elbow is not a long term solution.
Some basic strengthening work for the shoulder is often all that is needed to stop the compensations your body is doing that are causing the elbow pain. Your plan should be:
1. Stop doing what is causing the pain for a couple of weeks to let your body calm down.
2. Start developing strength and retraining proper movement patterns with the shoulder / scapula.
3. Re introduce activities that were resulting in pain.