Hey,

i have had the same (not recently though). The white thing looks like a small piece of cheese with very round edges. When you smash it it has a very pungent odour.
Basically, I think it is formed by food (or bacteria?) in the oesophagus. More exactly in the area of the epiglottis and the oesophagus. Do you have the feeling that food or pills get stuck in your throat? I have that all the time. I also get sore throat very easily. I believe this is due to small caverns in my throat - just an educated guess.