I wear a Band It on my right elbow all the time when I play golf. Have dealt with on and off issues with my elbows for 15 years. Have tried everything including the minimally invasive surgery called FAST (Focused Aspiration of Scar Tissue) which did not work for me.
I like the Band It because I have both medial and lateral issues with my elbow and the Band It helps with both.
The one thing I can advise is stay away from cortisone shots. Cortisone actually degenerates tissue and can make things worse. Of course if you have unbearable pain then cortisone may help but at a possible price down the road.
The reason this injury is so tough to heal is because what many people really have is probably tendinosis where the tissue is dead and it takes the body a long time to regenerate healthy tissue. But when it starts to feel better we start the activity that caused the condition and the scar tissue that has formed hasn't been replaced yet with the good or stronger scar tissue.
Anyway, eccentric exercises have shown some good results with some. Eccentric exercises lengthen the tendon as it loads the tendon as opposed to concentric exercises that shorten the tendon. Thera-band makes some rubber bars that can be used for these exercises.
Everyone is different and thus responds differently. There are some that respond well to rest and others that respond better with the exercises. The insidiousness of this injury is it can become chronic (as with me) and can take what seems like an eternity to heal. Tendons are tough to heal because they don't have the blood supply like muscles do.
Because tendons don't have elasticity like muscles do either, when they're over used they start to fray like a rope when it gets stressed beyond it's capabilities. These frays or small tissue tears then begin to die and the body tries to heal the tendon which takes forever in many cases.
BTW, what the Band It and other compression braces are doing is acting like a fulcrum. So instead of stressing the epicondyle tendon in the elbow it takes some of the load off the tendon.
It's not all doom and gloom. There's many cases that aren't as bad and come around quicker. Good Luck.