What could cause a sharp pain under both breasts while taking a deep breath?

Pleurisy: This could be something called pleurisy. It often happens after a chest infection like a cold. As the inflammation dies down, fluid is recycled back into your body. This process causes pressure and retraction on the muscles and connective tissue which is made worse on deep breaths. Try some ibuprofen, aleve, or tylenol (acetaminophen).