Hi! Welcome to healthcaremagic. I read your query. As you mentioned the molar fractured while extraction, are you sure it was not removed entirely? Usually no part of tooth is left in socket intentionally unless it is small enough to resorb over a period of time. Still for clarification or if you are having any symptom, i suggest you go to an Oral surgeon and get an X-ray of that area done. It will confirm if its still there and whether it needs to be removed or not. If it is causing any infection or pain, it needs to be removed. Do not worry, it will be painless under local anesthesia. As you had an unpleasant dental experience once, please dont keep that fear forever and go ahead. Hope the answer helps you. Thank you!