hmmmm.... that is a tough one. I would say run because I know that is what I would so, but I am not sure that is the best medical advice.
It is probably better to wait until you are breathing better before you do too much. Strength training and lighter cardio type work can be just as helpful when training for a race. Work on strengthing some other muscles and toning your core instead. You have some time before your race so it is probably better advice that you don't run. Work on healing before you get back into your running/training program and do something else to build muscle and burn the calories you need.