Is it possible it did get stuck and the coating wore off? The advil would irritate your esophagus, I've gotten advil stuck against my gum and it felt like it burned and left it feeling very raw. It could have also just hurt going down and caused soreness.
I would eat nonacidic soft foods for now, like pudding, etc. Also avoid hot/cold/ active yeast like beer etc would probably be a good idea in case you did damage or scrape your throat.
You could try gargling sea salt if you have access to some.
I'm not a doctor, but until one answers maybe this will help so you can eat something.