If your doctors have looked carefully and have found no evidence of heart, lung or large blood vessel disease, then the likely explanation is that you have what we call Chest Wall Pain. That is, chest pain that originates in the bones, muscles or nerves of the chest. A common cause is an undiagnosed rib fracture or separation of rib-cartilage from its attachment to the breastbone in the middle of the chest. If that is the case, the use of anti-inflammatory drugs, such as Advil® (ibuprofen), is appropriate.
The pain with exposure to cold air or with exercise does raise the question about a heart problem but the history of tenderness suggests that it arises in the chest wall and is musculoskeletal. If so, stress could make it worse.
The important thing is to be sure that the proper testing has been done to demonstrate that there is nothing wrong with your heart or lungs. Then you may just have to take anti-inflammatory drugs for a while.