In addition to an assessment by your physician, I would recommend seeing a physiotherapist.
Not only can they assist you with pain management, but they will also likely put you on a strengthening regime that with specifically deal with the Extensor Carpi Radialis Brevis (ECRB) muscle, the one most bursa in the elbow, olecrenon bursa, is on the posterior aspect of the limb.
Rest might be indicated in the acute stage, followed by light and progressive reps with hand weights. Again, see a physio for a personalized plan.