What is the white substance floating in my fresh mozzarella brine?
Those are just milk solids.

Quality mozzarella is sold floating in whey, the leftover liquid from making cheese.  While most of the milk solids are gone from the whey -- that's what the cheese is made from -- not all of them are.  As such, some will coagulate in the fridge, floating on top of the whey.

Now, if the floaters were any color other than white, or if they were fuzzy, that would mean mold.  But those are really just cheese bits.