Hello, I am Dr. Aditya Gudhate and try my best to answer your question. 'Chest tightness' has many causes, cardio-pulmonary, gastrointestinal and musculoskeletal. But you also mention difficulty swallowing, which seems to point to esophageal disorder. Please visit a surgeon where they will do a procedure called 'Barium Swallow' and 'Manometry'. If these are normal then your problem will probably be muscular pain. I hope you are satisfied with my answer. Get well soon!