Honestly, if it hurts that badly and you have insurance, go see a respected Orthopaedic surgeon - preferably one that specializes in elbow/arm issues. They will be able to give you a proper diagnosis and treatment plan to hopefully resolve the issue.
I am 36 and like you never had any injuries to speak of, until recently when I had some issues that I thought were symptoms of golfers elbow. It got to the point where I could not straighten my arm, so I went in and had it looked at. 15 minutes later I was told my issue was really triceps tendonitis, given a treatment plan, and within two weeks I was back on the courts. Your issue could be more or less serious than mine, but you really won't be able to know until have it looked at by a professional so you get the right diagnosis and recovery plan.