Hi Samantha, - it looked like flannel to me too so I was going to say that flannel naturally frays more, but the fix would be the same. Follow the advice of PaperPrincess with the fusible tucked under the fabric, and then if you have a decorative stitch on your machine, topstitch along the seams. I think it will add a nice decorative element and look like you planned it. Congratulations on your first quilt - I love the pink fabric with reindeer.