“Oral, plastic or other surgeon?”

I've always had "chubby cheeks" but as I've aged, just turning 60, the inside of my mouth is constantly bleeding from chewing on the inside walls while eating. The only reason I can think of is, as I've aged, I've lost the elasticity that previously kept the walls of my mouth out of the way. Would removing the fat pads from the inside help? What type of surgeon should I contact? Thank you.