Could the reason for the severe pain in left lower abdomen be a kidney stone? Would it show in CT scan as I had it done and nothing came out in c.T sca

May be... Have the possible diverticulitis of colon been ever considered? To get more meaningful evaluation, it's good idea to collect the feature, degree, and progress of specific symptoms over time with their sequence of events, and bring them to see doctor for review, analysis, more history, physicals, and possible tests as need so to deduce what is happening to you and how to treat you sensibly. Best..
Probably not. Kidney stones are diagnosed on ct scan. Can be missed if small. To cause such pain, then are large enough to be seen on imaging.