I've been suffering with this thing popping out on the left side of my throat for at least 10 years, I think it's the hyoid bone or thyroid bone popping out, when I yawn excessively and turn my neck, or swallowing while lying down, but lately it's happening randomly. It's quite alarming, I can't swallow or talk, it is very painful trying to swallow but I panic and it makes you want to swallow more. I push it back in, sometimes it works sometimes it takes longer, I have to calm myself and try to relax my throat. It aches after for a day or two. It happen yesterday and it feels like it's about to happen again any minute, one wrong turn or yawn and pop!
I have many other health issues which after reading others stories, maybe relevant.
I have hypermobility
Fibromyalgia
Lupus
Celiac disease
Chronic anxiety
Depression
Perimenopause
Low cortisol
Query hypothyroidism

I have noticed that it happens more when my anxiety is higher, due to tight muscles in the throat. Also when I yawn, the muscles under the jaw each side go into spasm, which is very painful and have to massage them out. My throat is quite slow too when I swallow, so anxiety is definitely messing with the normal functioning of the throat muscles and everything in that area. My doctor looks at me stupid when I try to explain what is happening, he said he's never heard of it, but my chiropractor has. It's such a horrible disorder, very worrying and painful, not knowing if it will pop back in is highly stressful and not great with the tight anxiety feelings in the throat already. It's a viscous cycle.