Is it normal to get lock jaw after a tooth extraction?

Not lock jaw: Lock jaw is a lay term for tetanus. You do not get tetanus from a tooth extraction. You can get infection of the tooth root or have a piece of infected retained root that can cause swelling of the surrounding soft tissues making it difficult to fully open your mouth. This should not normally occur after a tooth extraction. See your dentist.

Another Possibility: I agree that it would not be tetanus, an anaerobic infection generally from soil, commonly called lock jaw. The other likely possibilities are a strain on the muscles & ligaments of the TMJ (the joint the connects the lower jaw to the upper) or if it came on several days later, could be a "dry socket" where the blood clot is lost and the bone is exposed, releasing chemicals that are very painful.

TMJ: You are most likely referring to acute limitation of oral opening. Seen occasionally after tooth extraction. Most commonly wisdom teeth. Should resolve promptly, if not, ask extraction dentist. You could have an acute TMJ disk problem. If not resolved promptly, see oral surgeon for TMJ evqluation.