From Reddit:
Your oesophagus is lined with mucus, you couldn’t super glue something to it if you wanted to. I don’t believe it’s possible for gum to become adhered to it.
Is it possible you’re being paranoid?
Sometimes when you swallow a pill dry it brushes against the side and feels like it’s stuck in there, but really it’s not, it’s just a lingering feeling because the oesophagus is very sensitive.
Basically your options are ignore it and hope it comes right over time. Or you could go to the ER, wait 6 hours, get them to stick a camera down your throat, and possibly find out there’s nothing there.
If you’re not having any trouble breathing or swallowing, I’d recommend the former.