I have swelling under left breast on top of rib cage what could cause it?

Must see doctor: Any breast swelling in the breast or near the breast need clinical examination , possible mammography and other tests including if needed a biopsy . See your doctor with out delay

Could be from any #: of tissues in the skin, SQ or from the bone itself. I suggest you see a Surgeon so an examination can ascertain what's its most likely to be. A biopsy would confirm what it is? Good Luck.