What could cause pain in right side of chest?

Many things: Near the lower right side, are kidney, liver, gall bladder, duodenum, part of pancreas, large bowel as well as lower lung. For instance but not all inclusive, infection or trauma to kidney, liver; colitis distending large bowel; pancreatitis and gastritis; gall bladder disease, infection in lung, traumatic or inflammatory changes in bones. You should consult your physician for workup.

Various causes: Right sided chest discomfort may come from fractured,strained,irritated, or inflamed rib cage; pinched intercostal nerves which run between the ribs; pleurisy or lung disease; gall bladder,liver,esophagus problems; breast problems,etc. Detailed history and physical examination are needed for diagnosis.