What would cause your lower back to hurt and right under your rib cage?

Multiple causes --: From the back bone itself, like a disc prolapse, infection, pinched nerve from arthritis, or from a right sided kidney stone, infection, etc. Others maybe sprain of ligaments, muscle tears, fractures of back bone or rib(s). Abdominal lesions can be responsible. See your doc.

Several options: There are multiple potential causes, such as lumbar sprain/strain, kidney pathology, abdominal pathology, spinal disc disease, etc. See a physician for further evaluation.