My right jaw is going stiff, then clicking back and then going stiff again. is this lockjaw?

Not yet lockjaw: Sounds like your jaw muscles may be going into spasm and the clicking specially if painful could be a sign of TMJ dysfunction. Switch to a softer diet temporarily, jaw rest, moist heat should help. But you do need to be evaluated by a dentist familiar with TMJ problems. Or you could consult with an oral surgeon.

TMJ bruxism: Likely a TMJ problem. If stiffness accompanied by joint noises, locking or limited movement, "ear" pain, headaches, morning stiffness/soreness, difficulty chewing, bruxism, previous jaw injuries other other jaw conditions is a serious problem. See TMJ expert. Any dentist can be a TMJ expert with the proper training and experience. Mostly oral surgeons, prosthodontists, and orofacial pain docs.