Welcome to the board. The colors and fabrics you used are very pretty!
I'm a bit puzzled by your comment about "squares that allow for stretching",, however. Your quilt top should have little or no stretch. Before making up the quilt sandwich, you should press the top and backing really well. Spray starch is a good thing to use to help stabilize both the top and the backing. When you lay your backing batting and top out, you need to baste the entire thing with thread or safety pins every 3 or 4 inches unless you are using a big quilting frame. This keeps the layers from shifting if you just hand quilt or use a small quilting hoop.
I see a couple of options. Take all the quilting out and press everything really well and make sure you baste or pin the sandwich really well. Another option might be for you to tie this one.