"Baste" around the whole outside of the quilt with a short machine stitch 1/8 inch from the UNFINISHED edge and it won't ravel, nor will the batting come apart. It won't lose its shape. It will be a quilt without binding! and when you DO put the binding on, the baste stitching will be covered by your bidning!
This is what I would do if letting it air out for a while doesn't work!