What can be cause pain in lower back and abdomen on left side and coccyx pain after sitting for too long?

Don't Assume . Could be one of many things. Most likely it is what is called myofascial/musculoskeletal which should be reassuring. The fact that it hurts with sitting only is reassuring that more sinister issues not likely. However, the abbominal pain is a bit concerning with the back pain. Female issues, bowel issues and renal issues need to be ruled out. Your primary physician would be a good start.