Cut a small piece of the fabric, I usually do about 2inch square and light a corner of it on fire--use a candle or something stable. Let it burn for two or three seconds, being careful to do it over a plate or something non burnable. Blow out the flame and then let it cool a second or two. Now feel the burnt edge. If it is soft and smooth it is cotton. If it is hard and crisp, it is a blend or polyester or rayon. IF you smell the burnt part, the artificial fibers smell like plastic, also.
I like cotton for bed quilts, and use the other fabrics for tote bags, runners, wall hangings and craft projects.