How to fix my chin / labiomental groove? (Photo)

Chin sticks out, want it fixed. Surgeon said the chin (bones) is in right proportion to my face, and the part sticking out is only fat, and that the problem is really not the chin itself but the labiomental groove being deep and it's hard to fix. She said she could make an incision under the chin and liposuction / remove a little bit fat from the chin / remove excess skin but warned me that my submental space is kinda short and it might end up giving me a receding chin type look. Opinions?