I had this happen with jelly roll quilt. Luck was with me as I had not sandwiched it yet. I redid the seams where it was frayed. You could put some "Fray Stopper" on it (can get this at any fabric store) and then decorative stitch over it. My question is did you use a walking foot. If you don't have one, get one. This foot keeps fabric layers even when stitching.
I had my manual to my sewing machine and was able it order one online. I use the walking foot all the time now.