My Cheese Melted while in the Fridge?
My guess is that you don't have real cheese in your sandwich.

I've seen this before with things called cheese that were really types of American cheese. It happened when then product was exposed to moisture that it seemed to absorb, which then caused it to turn soggy and glue-like. If you'd have said that you had tomato in your sandwich, I'd have been sure this was what was going on.