The normal chest x-ray would rule out a pneumothorax, which is air leakage into the chest cavity with lung collapse, and, for the most part, the major causes of pleurisy. Pain, alone, can cause one to resist lung/chest expansion and be associated with the sensation of shortness of breath. But, if pain is not the only limiting factor, then other causes of chest pain, such as blood clots to the lung might also be a consideration.
The above not withstanding, the most likely cause of your pain is musculoskeletal pain, and this can originate in the ribs, muscles or ligaments of the chest wall. This type of pain does not generally last 5 to 6 weeks. The duration suggests that the pain may be due to nerve compression or inflammation. It might be a good idea to repeat your chest x-ray, with special attention to the bony spine, on the lateral view, regarding a compression fracture of a vertebra.
When any pain lasts this long it is usually a good idea to re-assess it periodically as the cause may become more apparent over time.
Good luck.