[Spoiler warning]
I don't think you'd get far prodding this issue with the devs; I'm pretty sure this neck 'sensation' is significant to the story and is something that they would have us discuss amongst ourselves. To answer your question though, I believe it is different/more than just Asterion's mental hang-ups. The scene where Asterion has a seizure has this:
Asterion laughs, and yet his throat constricts to choke him halfway through. A [ring of fire] burns around his neck. An unfamiliar pressure wells inside his chest-- expanding outward, like a star about to burst, until it becomes unbearable. He opens his mouth to cry out, and that's when he feels a hand brushing against the [burning collar] which threatens to strangle him.
This was during a playful moment with the master-- I doubt that it was triggered by remembering a traumatic memory. This is when we notice the birthmark too. Now you should see why the devs wouldn't want to touch this matter at all.
You are correct that Asterion was beheaded by Theseus though, and I also connect it to his first moments in the Underworld. The use of 'ring' and 'collar' is probably just an artful way of saying 'all around the neck'. It's also markedly different by being some sort of searing pain rather than some physical object. I've treated it separately from the tightening/constricting throat sensations, as these are just common literary expressions. Could be wrong though, just my two cents on the matter.