What causes severe sharp pain in the rib area on the right side just under the breast?

"Severe sharp chest pain" over the "rib area" especially with inspiratory efforts can represent pleuritic inflammation , as with an upper respiratory viral infection. See your primary care provider, as other causes may need further testing.

Pain can be indicative of something not functioning as it should. A simple exam can further identify where exactly the pain is localized and which if any tests need to be done to determine the underlying problem. You should see your in person Dr for an exam and testing. Organs in that area include the Gall bladder, Liver and Intestines.