I fell on icy steps, a week later the area where my floating ribs are is still painful. should i be worried or will this heal on its own?

If symptoms are get-: Ting better, then just continue with the pain meds, and start gradual twisting exercises of the body, slowly, within limits of discomfort and progress daily. If symptoms increase then see your doc. These ribs are surrounded by muscles, so sprained muscles are a common result of an injury. Warm/hot packs would greatly help. Good luck.