I had something very similar happen to me four years ago. I had a sort of run-of-the-mill respiratory virus for a few days. I woke up one morning with a clicking or popping sensation in my throat. It didn't hurt exactly, but it was a bit distressing. I could make the sensation stop if I turned my head to certain angles, but most of the time the popping sensation was present. I could also press on my throat and it would go away. My cold got better, but the clicking didn't go away. Eventually I consulted my PC doc, who sent me to an ENT. They scoped my throat and noted a bit of paralysis in my left vocal cord. They sent me to physical therapy (useless), prescribed speech therapy, had a couple of radiological swallow studies done (so they could see the swallowing mechanism in action), GI consults, etc. This was all probably over the course of a year, with no change to the popping sensation. Last year, on a third follow-up throat scope, they said the paralysis appeared to have improved somewhat, but I still had the popping sensation. Four years later it's still with me—no real change. I am mostly used to it now, but very rarely it will cause me a little bit of discomfort. In the end, the diagnosis was basically that the virus I had four years ago caused some nerve damage in my throat and that this will be a minor annoyance I'll just have to deal with.