It does not sound like it is originating from the heart itself.
If your chest is painful and tender to touch, it may be caused by a strained muscle in your chest wall. This can be surprisingly painful, but with rest the pain should ease and the muscle will heal in time.
If you have pain, swelling and tenderness around your ribs, and the pain is made worse by lying down, breathing deeply, coughing or sneezing, you may have a condition called costochondritis.
This is caused by inflammation in the joints between the cartilage that joins the ribs to the breastbone (sternum). The symptoms often improve after a few weeks and may be relieved by painkillers.
Anyway, it would be a good idea to see your GP, to rule out anything of more serious nature.