Can wearing a tight elastic bandage prevent my face from swelling too much after jaw surgery?

Yes: Elastic facial bandages, jobst is one brand, can help limit the swelling that results from mandibular(lower jaw) surgery. It is less helpful for maxillary (upper jaw) surgery. These surgeries will result in a certain amount of edema that will occur regardless of efforts to limit it. But certain surgical techniques, intraop meds, and the elastic bandage can help.