I mix cotton with lames on my sports team quilts all the time. A little lame or satin goes a long way. Please note my special handling of "shiny" fabrics. Most fray much more then cotton.. I back with light weight fuseable pellon. That jersey stuff doesn't last. Then I stitch all cut edges 1/8" from edger. Serging would work also. Besides the fraying pellon gives more stability. Also very impoirtant. I use a press cloth on anything not cotton.
Go for it, Have fun. I learn something with every quilt I've made. Become a fearless quilter.