I'm not sure what kind of Fairfield batting you purchased. I've made quilted home dec items out of their polyester batting. I don't love it as much as cotton batts, but I've washed it several times & with a bit of reshaping, it's held up okay. The nice thing about it being flatter is that there's less chance of it bunching up like higher loft poly batt.
I did also see their newer bamboo-rayon & cotton blend at my local JAF. I don't like rayon so I haven't used it yet, but it's what Caryl Bryer Fallert-Gentry uses on a lot of her quilts so obviously it has the potential to quilt up nicely. If that's what you bought, it should launder fine since rayon is less prone to wrinkling than cotton & generally provides good definition to quilting.
I prefer thicker, heavier cotton batting (W&P), but I have a friend who loves Fairfield 100% cotton and her quilts do fine in the wash even after years of regular washings.