Will a sliding genioplasty and a septo/rhinoplasty keep my mouth closed at rest? (Photo)

A sliding genioplasty can improve mentalis strain and lower lip incompetence, particularly if the vertical dimension in decreased and the horizontal dimension is increased. A septorhinoplasty will improve nasal airway breathing and may decrease mouth breathing but will not improve lip incompetence.

I believe, your xray shows mild case of vertical maxillary excess, which means your upper jaw grew down too much, pushing your lower jaw down and back. chin surgery helps you to close slightly, but jaw surgery is preferred to improve the over all aesthetics.

A rhinoplasty is performed to cosmetically change the shape of the nose. A rhinoplasty will not improve breathing out of the nose. A septoplasty  repairs a deviated septum, once medical necessity has been documented. A septoplasty will not change the shape of the nose.  There are many reasons patient's have nasal obstruction and keep their mouth open, which include a deviated nasal septum, valve collapse, vestibular stenosis, turbinate hypertrophy, chronic sinusitis, and allergies. Each one of these is treated differently with either medications or surgery to improve air flow through the nose. For many examples  and more information, please see the video  and link below

The sliding genioplasty will help with the mentalis strain and give better lower lip support.  Some patients are habitual mouth breathers and will continue to open their lips even at rest no matter what surgery is done.  Hopefully your rhinoplasty surgeon will take steps to ensure good nasal airway function at the time of the surgery.  The combination should give your a good cosmetic result as well as function.  Good luck.  Donald R. Nunn MD,DDS  Atlanta Plastic Surgeon