"Squeaky" homemade mozzarella
I may have found the answer I was looking for from 
http://www.cheesemaking.com/store/pg/242-FAQ-Mozzarella.html


  Many folks try to knead their cheese like bread during the stretching phase. That will result in too much moisture loss which can cause your cheese may become tough and chewy. Instead, you want to use a process more like pulling taffy.  Let it fall on itself a few times until it all seems smooth and shiny.


I was making dough at the same time and I think I might have gotten carried away with the shaping process and did it too much like dough.