My wife has sharp pain on right side under rib cage comes an goes for 2 days.. is it appendix or nothing serious?

Many possibilities: I always think of the worst possibilities: that's my job. If her pain increases at the "top" of the breath, that's called pleuritic pain - and can be a warning sign for pulmonary embolism (blood clot in the lung)! pain under the right rib cage can be related to gallstones. I have seen right upper abdominal pain related to appendicitis, but it is usually right lower abdominal pain. See the doctor.

See doctor: The causes of right sided abdominal pain are many. In upper abdomen, gall bladder, liver, stomach, small bowel, large bowel, and kidney can all contribute. Appendix symptoms are usually in the right lower quadrant of abdomen. Patient should see physician for physical exam and possibly testing.