Set it on fire. Really. Snip off a tiny corner, hold it with tweezers and set it on fire over a clean ashtray or the sink. Soft gray ash is cotton, a black hard ash is some kind of poly or other non natural fiber. If it smells like paper it's probably rayon. If it smells like burnt hair it's either silk or wool.
What you have sounds like a homespun though. Homespuns are a looser weave and they're woven from dyed yarns instead of printed after weaving.