Hi Stephen, firstly bowlers don't reallt get Wikipedia reference-linktennis elbow. Maybe more likely to be the other side of the arm (inside like in golfer's elbow?). But that said anything is possible.

Almost always problems in bowlers come from poor bowling mechanics combined with overuse (not enough rest, to many overs, poor diet, to much to soon etc). usually the training and playing regimen leading up to the injury will give some insight.

Right now rest will do nothing but lessen the pain until you begin to play again. I would suggest going to a good sports Physio who can show you how to apply some taping techniques to reduce the tension/load on the injured structure/s. There's many options depending on your problem. Then you need a video analysis of your bowling action, either by a physio or a bowling coach to look at what you are doing. A friend could even video you and you could take it in for viewing and discussing with the PT. A correction of the action should free the normal movement and the problem should resolve.

If that fails then there are other issues in place, such as energy pathways (meridians) etc that may be blocked and are reducing your normal healing response - delayed healing and normal use can lead to symptoms of overuse. Maybe go to London to the crystal palace physio practice and talk to the guys there as I am sure they could help sort you out. Would be worth the journey.

regards and best of luck