Nothing works as well as a steroid injection for these sorts of pains... especially the tennis elbow. See your doc!
The only problem with cortisone or steriod shots is if used on a fairly regular basis it can cause the bone to erode. I already discussed this with my physician. You run the risk on dependence on the shots as well. While it is the most effective way to help the healing process, it can also lead you to have surgery. It's all a catch 22. For arms and shoulders the shots are best...for hands, wrists, and thumbs, I'd try holistic or topical solutions.
Blue Emu is pricey. It worked for me for a while. Give it a try. Walmart has their version of Blue Emu...kinda stinky but, it felt good. The Stopain will work for over four hours an application. I found that since I started using it...I now use it less and less. I hope it is helping. I don't want to have surgery.