To prevent new towels from shedding first wash the new towels in the washing machine using hot water and a 1/2 cup of baking soda.
The baking soda and hot water wash will help stop the new towels from shedding when you go to use them.
You can also add some vinegar to the washing machine along with your regular laundry detergent when you wash the towels to prevent them from shedding after you've used them.