Would I qualify for a jaw surgery like CCW? Or is genio + rhino better? (Photo)

22F here. I had an expander + braces as a preteen, so my bite is fine. Due to mouthbreathing my jaws have grown down and look recessed. I do have TMJ/jaw deviation upon opening and trouble breathing from my nose, and lip incompetence. I tend to puff out my upper lip to breathe well. Reason I don't want genio + rhino is because I believe genio may make my face even longer, and the rhino might look strange if my maxilla is recessed.