Did not say how you got TE; certain exercises, only hurt when working out, job related or the outside chance that actually playing tennis caused it. Chaos & Local Hero are correct..... rest. And maybe applying a heating element like warning lotion, heating pad, alternate heat/ice packs, etc. while away from the gym.
If your still working out than might want to switch to DB movements, rather than BB's, for awhile. DB's allow a more natural twist(wrist/forearms), while BB's do not. As you said, pulling will bother it the most. If insisting on doing chins or BB rows, than use a false grip (thumbs in front of the bar) to avoid any hard gripping. It may or may not help, depends on the body reaction. Might try pullovers (bent arm or straight) to hit the lats if wanting to avoid any pulling motion. Also DL's and shrugs work the total back very well. Also keep the arms covered and warm. Applying a heating lotion (blood in the area), while working out, can help. Good Luck.