Left side jaw locking up?

TMJ: Usually signifies TMJ disk out of position. Can be a serious problem. Best option: see a TMJ-orofacial pain specialist. Any dentist can be a TMJ expert with the proper training and experience. Most commonly, oral surgeons, prosthodontists, and orofacial pain specialists. Ask your MD, your dentist and your dental society for referrals.

Disc displacement: You may have Temporomandibular Joint Dysfunction Syndrome with damage and displacement of the cartilaginous disc in the joint. See Dentist to determine cause (anatomical, parafunctional habit, malocclusion, hx of trauma, etc.) and treatment of the cause.