My parents just made fresh mozzarella, but they think that you don't have to refrigerate it. So right now there is about 12 lbs of mozzarella on my counter and it's going to stay like that for the next couple of days. Don't you refrigerate it?
It's cheese. the whole point of cheese is that it stays good without refrigeration.
that said, fresh cheeses have to be tightly covered or submerged in water or the outside will get gross and stinky.
wrap it in saran wrap nice and tight and don't worry about it. wash your filthy hands first tho