The quilt is lovely!
The only thing I can think of is that all the quilting lines are on the bias. Fabrics shrink most along the straight-of-grain (one more than the other, but I can't remember if it's the crossgrain or lengthwise grain that shrinks more). I'm thinking the solution would be to add quilting lines in the opposite direction, so that you don't have the long narrow strips of unquilted fabric.
I agree that pre-shrinking the squares before sewing would help the next quilt not do this. An all-over quilting pattern such as meander would also be likely to prevent skewing next time.