Had my voice box removed in 82 and shortly after it started feeling like I had a stick in my throat. X-rays while drink liquid showed that I had a pouch in my neck that would trap anything that was small.  Found that the easiest way to get rid of it was to drink a large amount of water to flush it out. all liquids will drain out the bottom is a short bit. When I go to a resturant I always ask for a large glass of water without any ice. The Dr said that it was divertilitus and he didn't think he needed to do anything to it. Over the years he has occassionally got a good cussing.