Since you are experiencing chest pains radiating to the back, that are initiated and made worse with coughing, sneezing, breathing (all structures of the chest wall move during these episodes), it is very possible that the cause for your complain is within the chest wall.
Actually, an inflammation or trauma to the various components of the chest wall is a common cause of chest pain or musculoskeletal chest wall pain.
The more common causes are costochondritis, traumatic muscle pain, trauma to the chest wall, “fibrositis” syndrome (fibromyalgia), referred pain, psychogenic regional pain syndrome, and arthritis involving joints of the breastbone, ribs and thoracic (chest) spine.