some form of interfacing is your best bet before you begin the applique process. however, since you have already begun, and if you want to continue with your current piece, I would try a bit of elmers washable school glue where the fray is beginning to separate from the main fabric (on the front and the back sides and allow it to dry on the surface of the fabric). My thought is that it may harden the fabric and hold the threads together as you work with it, but then will wash out with no problem in the end. Keep in mind I have never done this, so this is pure speculation!