I have had an issue for about 5 years with a burning pain that is very localized at dorsal to medial just above the Ulna, but does not extend to the triceps muscle. Brought on by any type of repetitive weighted pushing (push-ups, bench press, dips) over 5-10 reps depending on weight. Rest does not seem to be an antidote, as I have not been able to do pushing exercises in about 4 years. I was told by the VA that they thought is was Cubital Tunnel Syndrome, given a cheap elbow pad and sent on my way… Trying to find a way to get back to pushing weight.
Get into the website and get to the “I have pain” page and start working on the elbow and above and below the elbow, particularly if it is something with the nervous system, that nerve goes from the neck down. As far as training, you should start with light loading and rep ranges that do not seem to aggravate the area and build volume through multiple sets instead of multiple reps.