That sounds like something I dont want. I once had a Schatzki ring. It was horrible. Without warning food would just stop in the esophagus. Sometimes drinking something would clear it pretty quickly but sometimes it wouldn't and it is a horrible feeling. My dad had one fixed last month. They run a rod down into the stomach then run a inflatible down the rod using little rings, then they inflate the balone thingy and you gag the whole time they inflate it... I hope I never have to do that again, and I hope you don't.
I really hope this is an easy fix for you because I am sure it really is a PITA. I looked it and read about it, it sounds distressing and painful. Prayers offered for you and your doctor.
Julien