A 38-year-old female office worker presents to an outpatient clinic with persistent right elbow pain. She reports that the pain began insidiously about six weeks ago and has worsened, making it difficult to perform daily tasks like typing and lifting a kettle. She recalls no specific acute injury but notes that her work involves extensive computer use and occasional lifting of heavy files. The pain is localized to the outside of her elbow and radiates down her forearm. It is exacerbated by gripping objects and extending her wrist against resistance. She has tried over-the-counter pain relievers with minimal relief. She denies any numbness, tingling, or weakness in her hand or fingers. She has no significant past medical history and takes no regular medications. On physical exam, her temperature is 37.0°C, blood pressure is 118/72 mmHg, pulse is 78/min, and respirations are 16/min. Oxygen saturation is 98% on room air. There is notable tenderness over the lateral epicondyle, and pain is exacerbated with resisted wrist extension and supination. Gripping strength is diminished due to pain. Given her presentation, what is the most likely diagnosis and the appropriate initial management strategy?