What kind of jaw surgery could fix my receding chin and lip incompetence? (Photo)

The photograph demonstrates a weak chin profile. A Silastic chin implant can be inserted on the front part of the mandible through a sub mental approach to give augmentation to the chin. This will help with facial balance and proportions. There are many reasons patients have difficulty breathing out of your nose such as allergies, turbinate hypertrophy, a deviated septum, valve collapse, vestibular stenosis, and chronic sinusitis. Each one of these issues are treated differently with medications, or surgery. For more information and many examples of chin implants, please see the link and the video below 

While your ideal treatment would have been a lower jaw advancement as part of your orthodontic treatment program, that option has now passed when your teeth changed to your present bite relationship. You now need to consider a sliding genioplasty to move the chin bone forward to improve both your profile and your lip incompetence.

There are two options: jaw surgery, chin surgery. Jaw surgery is probably the best solution, but you would need to go through braces again for about 6-8 months. Chin surgery will make your profile better and it takes less time. 

Your orthodontic treatment has unfortunately considered only 'fixing the bite' and has not managed the fact that your lower jaw is smaller than the upper jaw. Extracting teeth does 'compromise' the facial profile. You could have a masking procedure without orthodontics to improve the jawline with augmenation implants; or undergo more orthodontics to 'essentially try to reverse' part of the previous treatment and then undergo a jaw advancement to get the better result. Consult a maxillofacial surgeon. We see this very frequently and it can be improved.