Skinny with a double chin, what are my best options? See details below. (photos)

I am 5ft7 and 95 pounds but I have a double chin. I had lost weight, then regained to my current and feel like the weight always goes to my chin. I have a history of extreme anorexia and bulimia, now getting better but can't face the chin issue. My dermatologist said Kybella may not work for me. The area, she said, looks like loose skin and little fat. It's not saggy, it's a blob of soft flesh. Best options? I'm only 34 and highly distressed. I fear if I keep gaining more chin fat will too!