I think that some soft tissue work around your elbow is a good idea, along with having a coach make sure your grip is perfect are my initial recommendations. Seeing an ortho hand specialist to get a steroid injection is something I'd recommend too.
Finally, supplementation outside of nsaids are mostly a wash. Glucosamine, cissus quadrangularis, and other topical analgesics do not have lots of good data. I think a warm elbow sleeve may help, however.