You don't need machine quilting thread to quilt; regular thread works fine.
Are you trying to do free motion quilting? Since you covered the feed dogs, I assume that's what you are trying to do. If so, you *must* have a "jumping" foot. Most people use the darning foot. This foot lifts up between each stitch to allow you to move the quilt sandwich. It sounds as if you are using your regular sewing foot. You can use a regular sewing foot to quilt (similar to using a walking foot, with the feed dogs up), but *not* to free motion quilt!
Most likely one of the plastic feet is a darning foot. Look for one that has a spring action on it. Holding it in one hand, you should be able to move the foot up and down with the other hand. That is because it has a spring in it.
If you have been using a regular foot to try to free motion quilt, that explains why you are having such difficulty moving the quilt sandwich.