Orthognathic surgery or should I have orthodontic with TAD to correct overbite with incompetent lips?

Orthodontic treatment should not be  used to replace jaw surgery. It might correct your bite but your profile might suffer. Please see a board certified orthodontist. 

TAD or
temporary anchorage devices are great tools in the world of orthodontics but
braces are not a substitute for orthognathic surgery.  Braces are designed to correct misalignments
in your teeth that cause malocclusion.  Sometimes orthodontic treatment can help improve the appearance of the
middle to lower face but if the asymmetry that you are unhappy with is caused
by the bony structures of your face and jaw then orthognathic surgery
would be your best option.  There is also a possibility that you would require orthodontic treatment in conjunction with
orthognathic surgery to help you get the look you wish to achieve.  However, in order
for me to say with any certainty which procedures would work best for you I
would have to perform a physical examination.  My recommendation for you is to research for a board certified oral
maxillofacial surgeon to find out if you are a candidate for orthognathic
surgery.  Your surgeon can also refer you
to an orthodontist who has experience working with patients who are preparing
for orthognathic surgery if needed.Be well and
good luck!@norrisplastic