Yeah, does seem like tennis elbow (lateral epicondylitis). It’s caused due to inflammation of the tendon that attaches to the outside of the elbow, due to overuse of the wrist extensors. I am not sure if wearing a band would provide a solution, since it only kills the symptoms and could put additional pressure on support joints/tendons which would then have to bear any load. Further, the problem could resurface in time and trouble other areas which share the load to reduce burden on the affected area. Pain caused due to sports injury is mostly by way of referred trigger points, which is usually the root problem.
Extensive research has been done on myofascial pain and trigger points by doctors Travell and Simons. They have released two volumes on the subject. You can look those up on Amazon or just google Travell and Simons. You could also visit triggerpointbook.com - a stripped down version of the scientific literature for the layman. Look this book up on Amazon and read the reviews. I once suffered from shoulder impingement and tendonitis. Tried bands, rehab, RICE but any relief was temporary. Got hold of the book and it did work.
There are a lot of well researched articles on the subject of trigger points. It’s an area worth exploring since injuries are all so common. Here’s a link to get you started -
http://www.sover.net/~devstar/trpdef.htm