There is no way that you are going to have a heart attack over this issue. Heart attacks are caused by a lack of blood flow to the heart muscle itself.
Well Chostochondritis pain does mimic the pain of a heart attack, though it shouldn't cause one. If you have new, severe pain or other symptoms of what can be a heart attack, then get it checked immediately. Otherwise, it's all pretty normal with the condition. You can use over the counter pain meds and a heating pad to help with the discomfort in the mean time. good luck.