When I yawn or take a deep breath, I have a sharp pain in my stomach. Is there something wrong with my digestive system?

Maybe. Sounds like a spasm of your diaphragm (breathing muscle). This is similar to that "side stitch" pain many people get when running. It could be your GI system though, so you should have it checked out.
Probably not. This pain may arise in the abdomial muscles. However, this might be a symptom of a hiatal hernia in which the upper portion of the stomach protrudes through the diaphragm into the chest.