What kind of surgical procedure do I need to correct my face/chin? (photos)

You have a very short chin and a resultant mentalis strain. You would be best treated in the long run by a sliding genioplasty that will permanently move the bone forward and improve your facial profile and relieve the mentalis muscle strain. This is a procedure done from inside your mouth so there are no external scars.

 The photographs demonstrate a weak chin profile. To augment the weak and recessive chin, a chin implant is inserted directly over the bone of the mandible through sub mental approach. Chin implants are manufactured in a variety of sizes and shapes, are inserted under local anesthesia as an outpatient surgical procedure. For more information and many examples, please see the link below

You should evaluate your "bite" as well since you have a high angle growth pattern which explains all your concerns. The upper jaw is typically overgrown vertically and the lower jaw grows at a steep angle causing the lips to separate. The chin is recessive since the jaw grows downward not as much forward. Typically a surgery on the jaws are recommended with a genioplasty and possible ramal/ jawline augmentation. Consult a Maxillofacial surgeon.