What treatment would be best for my deep labiomental fold? (Photos)

I have a very deep fold and a round chin. I had a surgeon recommend injecting fat into the fold however I’m worried my chin will just look big and stick out more. There is about half a cm of fat on top of my chin bone so maybe that can be reduced to give a more flat appearance too? I Any recommendations that I should look into will be great. The last photo attatched is a sort of desired outcome. Thanks :)