There are a number of causes of the "burning sensation" you have experienced, including "heartburn" due to
gastroesophagealGastroesophageal reflux disease
Gastroesophageal reflux in infants reflux disease (GERD) and, especially when related to exertion, coronary artery disease. Your pain is really not suggestive of the latter. Nor is it pleurisy.
The most likely cause of this sensation, as your primary care provider (PCP) suggests, is musculoskeletal or the pain of neuritis, the latter caused by either compression or stretching of the nerves that serve the involved burning areas. It should be treated as such. The compression could occur anywhere, from where the nerves emerge from the spine to the more peripheral nerves.
One final thought. In the early stages of herpes zoster, commonly called shingles, one may experience pain up to 96 hours before the skin lesions appear.