What are the white spots on my cheese?

It is calcium lactate crystals. It is safe to eat. On hard cheeses it is a sign that it is aged well and a fine gourmet cheese.
 
Those bits are called tyrosine, and they’re actually amino acid clusters that form with age. Tyrosine clusters are signs of a well-aged cheese, which is why you’ll find them in some of the world’s most loved cheeses like Parmigiano Reggiano, aged goudas, and mountain cheeses like gruyere.  
Tyrosine is a non-essential amino acid found mainly in casein, the dominant protein found in milk. The word itself is from the Greek tyros, meaning cheese. 
Tyrosine lends a distinctive textural charm to cheese, and is a welcome interruption within the body of an otherwise smooth texture. Sometimes it even compliments the beverage you may be drinking with your cheese, as in the case of pairing a full-bodied stout with a super-aged cheddar; the crunchiness of the cheese somehow matches the fullness of the beer by contributing its own textural intensity.
Tyrosine is not to be confused with the crunchiness you can find in some washed-rind cheeses. Since this category of cheese is usually washed in some kind of salt water brine, residual salt crystals are often left behind on the crust of these cheeses. When you take a bite of rind and inner paste together, the crunchiness from the outside can be mistaken for existing on the inside.

Now go and impress your cheese-loving friends with your new vocabulary word!
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For the Cheese Nerd here's more...
https://www.cheesescience.org/crystals.html
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