You can actually buy diaper fabric. I got mine from Joann's. I use it to make dish towels and haven't noticed any pilling.
Living in Saudi Arabia back in the 60's and there were no diapers to be bought so I got a bolt of medium weight Muslin material, after two washings with bleach I had perfect diapers!! Try muslin material have fun!!
I've made many burp cloths out of diapers from Wal-Mart, but never used them, and didn't know about pilling. Uh-oh.
I always wash first because they are cotton and shrink and I don't want the designs to be messed up from shrinkage. That's how I know about the pilling.
My Walmart's were Gerber brand. Sometimes they have the prefolded with the padded center, and sometimes the flat.
My daughter-in-law called me last year when a sale was happening at Walmart and they were clearancing out some prefold diaper--I told her to buy me several pkg. They are upstairs in a box. They are trash as far as I am concerned--they are ripping out at the seam in some I opened to look at and not even washed yet. Was also going to do burp clothes with them--the only way that will work now is to hide that shred ripout place with wide ribbons or pretty fabric. The Birdseye Brand I think is what JoAnn's has and I do like that with a layer of good flannel between the outer and inner pieces.
I no longer know much about diapers. Have you checked Amazon?