It sounds like medial (closer to the body's midline), as opposed to lateral (outside) epicondylitis. Otherwise known as golfer's elbow and tennis elbow, respectively, where tendinitis develops in the elbow ligaments.
Rest and using ice or heat or elevation to reduce the inflammation is the safest, most effective solution there.
Although sometimes simply switching from a prone (palms down) to a supine (palms up) or neutral grip for pulling movements can usually help a bit.
If it gets worse or doesn't seem to improve, you may want to visit a physical therapist or chiropractor for the proper stretches and soft-tissue exercises to do to get yourself out of pain. Be wary of using a fitness solution to solve a medical (orthopedic) issue. Hope this helps.
