I'm not 100 % positive but I think if you snip off a small piece and light a match to it, if it turns to ash its cotton, if it just kinda melts into a ball its synthetic. They did a show on this at Simply Quilts so if you went to HGTV and did a search maybe you'll learn more.
I went and searched and This is all I found. They have changed their search.
Burn Test: To identify fabric content, burn a corner of a piece of scrap fabric and extinguish it in a bowl of water. Cotton will feather with a light ash as it's burned; poly blend will feel like plastic when it is burned.
The tear test also works. 100% cotton will tear to the true grain and if it is a blend it won't. That's why some quilt shops will tear the fabric instead of cut. The better the fabric, the better the weave, and the straighter the tear.