Good job! There is a paper piecing technique that uses freezer paper instead of regular paper. As I recall, the way it is done involves ironing the fabric piece to the paper, then fold the paper back along the stitching line and stitch very close beside the fold but not actually on the paper, then add next piece of fabric the same way. When you're done, you can peel the freezer paper off and reuse And since you never actually stitched through the paper you don't have all those little bits of paper caught up in the stitches to deal with.
Anne Peterson has a lesson on doing this kind of paper piecing in one of her Craftsy classes.
Rob