Someone mentioned the burn test. If you don't know what you're looking for:
If it's 100% cotton, when the fiber is burning, it'll smell like burnt wood. Cotton is a plant.
If it has some polyester in it, you'll get some melting in there.
In case anyone wants to know - if you burn 100% wool, it'll smell like your hair burning - but then, you are burning sheep's hair.
If the fabric has polyester in it, the wrinkles might be heat set in from too hot of a dryer maybe??? If the wrinkles are heat set in, don't know if they'll ever come out.....