Have a very sharp pain under left rib cage going through to a throbbing back ache?

Chest?: It is difficult to tell what is exactly the problem without knowing what other symptoms you are having. Is there shortness of breath, nausea, vomiting, sweating? If so then you need to go to the ed in order to rule out any cardiac issues. Other possibilities are abdominal problems which cover a number of issues. Also muscular and rib inflammation which carries no danger to life. Get checked asap.