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This looks like tendinitis of elbow (Golfer's or Tennis' elbow).
The Golfer's elbow has the pain on the inner side of the bone on elbow (and its counterpart tennis elbow on the opposite end, both have same treatment) and has following advised for the treatment;
1) Anti-inflammatory analgesics like Motrin / Advil for around 10-14 days.
2) Elbow brace
3) Physical therapy
4) Warm compresses
5) Local analgesic patch / ointment / spray
These are the initial modalities and if the pain does not respond than the further interventions would be required;
1) iontophoresis, phonophoresis
2) electrical stimulation
3) shock wave therapy
4) local steroid shots
Read the resources;
Please feel free for your follow up questions.