Did you use a fusible to hold your fabrics together before you stitched? What kind of stitch did you use?
If you are using a fusible (like heat and bond lite) and a machine satin stitch, you should not have any fraying when washed. If you are using a blanket stitch and the quilt is washed repeatedly it may fray a tiny bit over time. I do not know of anything to spray on to keep it from fraying. Even fray check (which will make your edges stiff) will wash out eventually.