What's it feel like, and what does it look like? Cotton and linen have very little elasticity, kinda like rope. If it has some stretch and recovery, the most likely fibers are wool and acrylic. A burn test can supposedly distinguish between the two, but I've tried this myself with scrap wool, and it was hard for me to tell. Basically, you burn a piece of yarn, and if it melts into a hard bead it's acrylic, and if it turns into an ash and smells like burned hair, it's wool. Try Googling "fiber burn test." There's also bleach. Apparently, wool will dissolve in bleach and acrylic will not.
You could post a pic. Someone might recognize it.