Pain underneath my right shoulder, pain while breathing deeply. Why?

Referred Pain? The same nerves that innervate the diaphragm go to the shoulder, as well. Therefore, anything that irritates the diaphragm, such as gallbladder or liver problems, can be "referred" to the shoulder. If the only symptom is shoulder pain (ie, no abdominal pain, nausea, vomiting, etc), I would search elsewhere. Lung problems such as pneumonia, pleurisy can do the same, although less common.