Is it 100% cotton??? It sounds like it's a cotton blend...like blending cotton with angora, or another combination. I had this happen to me, too, but the yarn was a blend. Debbie Bliss Cotton Angora! Bah! It acted up just as you're describing. And it pilled like crazy, too, and didn't hold it's shape either.
Later on, I read a review about this yarn. On Knitters Yarn Review. She spoke about how blending cotton with an animal fiber can be tragic.
Noro has been pulling this lately, too. Tossing in a certain amount of cotton. Ugh. Cotton and animal fibers are not a great pairing.
You didn't mention your cotton by name. So I'm just relating my experience with cotton blends.