There is a chance that you subluxated (partially displaced) a rib. This usually happens in the back from a traumatic incident, and can cause restricted and painful breathing. You also might have strained or bruised an intercostal muscle, located between the ribs. Either one would cause the symptoms you're describing.
A chiropractor might help, as well as alternating heat and ice on the area. Start with 10 minutes of heat, end with 10 minutes of ice.
Gentle deep breathing exercises can help a displaced rib readjust. Follow the procedure in the link below, except only breathe in to the point where you experience NO pain. You will find that you can breathe in deeper the more you do it.