I use the burn test.
I light a candle and get an ash tray handy. Also a glass of water nearby - just in case. It is better to do this outside - the burned smell can linger inside the house.
I cut a snibble of fabric - about 1/4 inch by 1 inch is plenty large enough - and hold it with tweezers into the flame until it ignites. Poly (and other petroleum based fibers) will burn with black smoke and usually leaves a hard ash. The residue stays hot longer than the residue from cotton. Cotton leaves a soft ash. I put the burned fabric in the ashtray.
I can't tell rayon from cotton, though. Wool smells like burning feathers.
I will occasionally get a cotton/poly blend that I think is 100% cotton - but it is a blend.