Adding to the community of *this happens to me too*. For me, it isn't painful and I can still talk. I don't panic but that's probably due to it not being so painful for me. I, like OP, feel it right above my adam's apple and to the edge a bit, near the pulse spot. I can poke around in there and usually get it back into place. Sometimes it takes longer than usual.

I feel like we should start listing our other weird undiagnosed symptoms, in case we have additional overlap. Could help people, who knows. To preface, I'm getting checked for hypermobile ehlers-danlos syndrome.
So without making this too long:
- hypermobility in many joints (double jointed)
- chronic fatigue
- pain in knees, hips, lower back, feet
- post nasal drip (pretty much had it for like 7 years now)
- depression, anxiety, adhd
- dizzy when standing after sitting, black tunnel vision when standing quickly after sleeping
- extra stretchy skin
- For a short period of time when I was 16 (maybe a few months at most), I had excruciating headaches that sent shooting pain right down my neck into my shoulder.
- I've always gotten random shocks in my neck that are very short and quick but extremely painful, like a quick electric zap.