It is a common practice to SITD around each block smoothing the top square as you go before you add any additional quilting. This stabilizes the top, and squares it up. If you have extra fullness in some blocks, you can decide on a dense quilting pattern to take up the excess.
Are the completed rows 'frowning' also, or just the rows to be quilted? At this point, where you have already begun quilting, it's hard to say what to do. I personally would pull the ends up to make the rows square, quilt the center of the quilt and leave the borders till last. You can cut an additional piece of batting that will just go under the borders to take up any additional fullness, then use a piano key quilting pattern that allows you to ease fullness in as you go.
I also congratulate you on quilting it yourself! It's a learning experience, and your next one will be better (it also give you an appreciation for your long armer!)