First, welcome to OCF. Im sorry to read about the loss of your aunt and your father. Im not sure how much of a role genetics plays in oral cancer.
A sore that is there for longer than 2 weeks should be checked out. You were right to see your dentist so they can take a good look at it. Your dentist may refer you to an oral surgeon or an ENT for a biopsy. The way to tell if its cancer is thru a biopsy. Besides smoking and drinking, oral cancer can also be caused by
HPV and for a very few, there is no known cause.
Congrats on being smoke free! Quitting is not an easy thing.
Hang in there and try not to worry. If you need a biopsy, by the time you get the appointment til the results come back, it could be a few weeks.