You can get something they call intercostal
chest pain, or bruised ribs, where you have
pain in your rib cage which makes it hard to breath. If its something like that, it normally gets better.
There are more ominous things that can go on in the heart of course, just like there are creepy crawly things that run about in the night. Examples include prinzmetal angina and pericarditis. For the most part though the things that are really there are a whole lot less scary in the day time.