Jaw surgery with a mandibular advancement can permanently improve your facial profile, jaw line and the way your upper and lower jaws come together. The benefit is that the results are dramatic and last a lifetime. As you mentioned, the recovery can be involved and requires you to have a special diet for up to 6 weeks. And, there is a risk of permanent numbness in the lower lip and chin. This happens to some degree in up to 10% of patients. Your individual risk depends on age, technique and the planned movement of your jaw. Many patients who have some numbness after the surgery still report that they think the surgery was worth the risk because they are very satisfied with the overall outcome of the surgery.
It looks like there may be a bony asymmetry. Sometimes this requires full jaw surgery and sometimes it may be fixed with just a chin surgery or genioplasty. A full evaluation of you entire jaw and facial skeleton will allow me to make a diagnosis and treatment plan. It's important to see the whole jaw because the posterior lower jaw or the jaw joint could also be causing the asymmetry. Camouflage with fat or filler is also possible if there are no other issues with the jaw.
During jaw surgeries where the upper jaw is moved forward, the skin over the bony nose widens because it is essentially be stretched forward to accommodate the new jaw position. This procedure is not done specifically to widen the nose unless you have jaw issues. The attachment of the nasal base to the bones can be released through an incision in your mouth to achieve some widening. This alar release procedure or a revision rhinoplasty/alarplasty may address your concerns better than a jaw surgery. A clinical exam would be needed to give you the best treatment plan for your specific situation.
It looks like the braces were used to try to camouflage your underbite to avoid surgery. In your case, the jaws are not aligned properly. Your lower jaw has grown more than your upper jaw. The only option to predictably fix this without having relapse is to have orthognathic jaw surgery. Based on your consultation and workup, I would be able to assess whether or not you would need to be in braces or Invisalign in conjunction with jaw surgery.
Your jawline is very well defined and in the ideal position. From the photos, your chin projection is not as developed as your jaw. A chin implant or genioplasty may improve the balance in your lower jaw and chin. If you don't have any problems with your bite (the way your teeth come together) then a chin-only surgery may be the best option rather than jaw surgery. An in-person consult would allow me to assess your proportions and provide you with the best treatment plan to achieve jaw balance and symmetry.
