I think both the thicker fancy stitch or hand sew would work great! So sorry about your problems......it could be worse,I know from some of my mistakes. Would love to see a full picture of your quilt, it looks beautiful.
Welcome to the Quilting Board!

I think both the thicker fancy stitch or hand sew would work great! So sorry about your problems......it could be worse,I know from some of my mistakes. Would love to see a full picture of your quilt, it looks beautiful.
It is easier to be wise for others than for ourselves.
I'd handstitch them. I don't think you'd notice it.
I'd use fray-check on the frayed edge, put the fuseable interfacing under the area, and top stitch with a very narrow zig-zag stitch.
I had this happen with jelly roll quilt. Luck was with me as I had not sandwiched it yet. I redid the seams where it was frayed. You could put some "Fray Stopper" on it (can get this at any fabric store) and then decorative stitch over it. My question is did you use a walking foot. If you don't have one, get one. This foot keeps fabric layers even when stitching.
I had my manual to my sewing machine and was able it order one online. I use the walking foot all the time now.
It just looks like some of the seams got a little narrow. That's okay! It has happened to all of us at one time or another! Just lap the side with the most fabric on it over the other side, then hand or machine stitch over it. If you want to really cover it and don't have any more fabric, just remember that all fabric in a quilt usually doesn't come from the same line. You could also use bias tape or rick-rack to hide it. There are bunches or creative ways to cover our booboos. You did well for a beginner. Just keep it up!
If you need to fiddle with it to get it all lined up before stitching down, I'd use Elmers SCHOOL Glue...the school glue is actually a thick starch and will wash out easily. But, meanwhile, you can adjust and press with your fingers until you have it just right.Then iron it down, using a piece of parchment so your iron doesn't get sticky and proceed to stitch it tightly. Every quilt gives us it's own lessons!
Thanks again everyone! I'm heading out right now to my local craft/sewing store for some Fray Check and a fusable interface! I will keep everyone posted!