My upper lip sticks out and looks swollen, I have a deep overbite. Would braces or lip surgery help? (photos)

You have a forward head posture and a recessive chin which makes the upper lip appear more protrusive.I suspect you also have a narrow maxilla and airway issues as well.  Are you getting sinus issues, earaches, clicking or popping TMJoints or headaches and how is the quality if your sleep.You seem like an excellent candidate for a DNA Appliance and Expansion orthodontics.  Never consider extraction / contraction orthodontics.I would correct the posture and structure first and then evaluate the lip for surgical intervention after improving underlying physiology.The web references are patient videos.Ira L Shapira DDS, D,ABDSM, D,AAPM, FICCMOChair, Alliance of TMD OrganizationsDiplomat, American Academy of Pain ManagementDiplomat, American Board of Dental Sleep MedicineRegent & Fellow, International College of CranioMandibular OrthopedicsBoard Eligible, American Academy of CranioFacial PainDental Section Editor, Sleep & Health Journal
Member, American Equilibration SocietyMember, Academy of Applied Myofunctional Sciences