Hi, welcome to the forum, the possibilities of such pain are Costochondritis (usually experienced on left side), Slipping rib syndrome (ribs can slip and impinge on the intercostal nerve, producing pain), Precordial catch, pleuritis and Neurologic disorders (radiculopathy).
Other causes of back pain like diverticulitis, irritable bowel syndrome, kidney infection, kidney stones, and bowel problems like constipation, pain arising from muscles and skin over left side abdomen.
Any history of trauma to the chest should be noted down. You need to undergo radio imaging (MRI/CT), urine analysis and as well as ECG (cardiac causes) to rule out the above causes. I suggest you to consult physician and get evaluated. Take care and regards.