This kind of stuff is pretty common in people who don't transition conservatively into this kind of training. If you make a large and abrupt increase in any activity, you're going to get beat up. I would back way off the overhead/elbow-related work for a couple weeks to get the inflammation down. During that time, continue with the mobility work for the entire body - any poor positioning can contribute to pain in seemingly unrelated body parts.
When the pain is gone or at least very minimal, begin increasing the volume and intensity of the exercises that were removed, and do so incrementally and conservatively. More often than not, it's not the volume or intensity itself that is causing the problems, but the abrupt increase. If you can build back up to the full level gradually enough, you should be able to get conditioned for it and do fine.