Pain at the right side of the neck, just under the jaw. is it it fatal?

TMJ: Pain is most typically not a fatal medical issue and it is not productive to jump to that conclusion as a first thought when you have pain. If there is nothing else going on (neck mass, weight loss, fever etc) i would think this is probably tmj. This is all the more likely if you chew gum, crunch ice, or clench your jaws at night. See your doctor or a dentist if it doesn't get better in a week.

It depends: The odds are you don't have a fatal problem, but it needs to be evaluated. You need to speak with an ENT doctor.

Jaw Pain: I have never seen a fatal jaw pain. The pain in the jaw that can lead to fatality is related to rapidly spreading infection as in venous sinus thrombosis or a space infection that spreads down into the mediastinum to the heart. Typically that is treated by an oral surgeon or ENT md in the hospital with IV antibiotics.

Unlikely: Unlikely. See your MD ASAP if you are concerned.