I would strongly recommend that you see a doctor
. This should be evaluated as it could be a sign of a serious problem.
What you are describing is known as pleuritic chest pain or pleurisy. The pleura is is outside lining of the lung. When this gets injured, it can cause diffuse pain around the lung as the pleura has a lot of nerve fibers that can transmit pain.
There are a couple of causes of pleural injury
. One to worry
about is known as pulmonary embolism or PE. A PE is a blood clot that gets stuck in the lung. This can be very very dangerous as it can limit blood flow to the lung. Another common cause is a viral infection of the pleura. Another common cause is a pneumonia.
Chest pain in general can be a sign of a serious problem. The chest, as you know also contains the heart, so any chest pain makes us worried about heart problems.
Please get this evaluated. The fact that you are also short of breath is very worrisome. This should be addressed. I would avoid swimming till you have this evaluated. While swimming should be fine once cleared, do not stress the system until then. Good luck!