When you attached your borders on the quilt, did you measure the length needed and cut the pieces to fit, or did you just put a strip of fabric on top of your quilt and stitch until you got to the other end of your quilt?
Quite often, there is more give and stretch in your border than there is in the pieced blocks of your quilt. If you are not measuring your borders before attaching to your quilt, you will want to make sure you are pulling it somewhat snuggly. Otherwise, it's like you've attached a ruffle.
I've had more than my fair share of ruffled quilts in my early days. Good luck!