Thank you all for the feedback!! I think I have a pretty good idea of what to do now and I defnitely feel better about my oopsie! Do you guys think I should add some more quilting so they are closer together or if I just do some sort of stitch over all seams that would be enough?

Contgrats on your first quilt!!
You can also get some light weight knit fusible interfacing. Tuck it into the quilt, with the fusible side up, then pin the fabric in place, as the other posts directed. USE A PIECE OF COOKING PARCHMENT< OR A NON STICK PRESSING SHEET on top of your quilt, then press according to the instructions for that interfacing. This will stablize the fabric. I would then stitch over it. Be sure to put something between the iron and the quilt or you might get stuff on your iron.
I would do sort of a wiggle stitch over the seams if you think that there may be additional areas that had a slightly too small seam. Just a wave that crossed back and forth over the seams.

On my computer this fabric looks like flannel. If it is, that may be the problem as flannel usually frays more than cotton quilting fabric. I'd follow the suggestion for using the fusible and then using a decorative top stitch. If you use flannel again use a wider seam allowance.

I agree with Buckeye Rose, you really need to quilt more. If you read the quilt batting package, it will tell you the maximum distance apart that your quilting can be. Most of the 70\30 and 80\20 cotton blends need to be quilted 4-6 inches apart. Some brands will let you quilt farther apart than that. I really like the colors of your quilt and it should last you a good long time with a little more quilting.

The fabric is not flannel.
The quilting is only 4 or 5 inches apart at the very widest parts too...

Hi Samantha, - it looked like flannel to me too so I was going to say that flannel naturally frays more, but the fix would be the same. Follow the advice of PaperPrincess with the fusible tucked under the fabric, and then if you have a decorative stitch on your machine, topstitch along the seams. I think it will add a nice decorative element and look like you planned it. Congratulations on your first quilt - I love the pink fabric with reindeer.

Thanks again everyone. As I said I'm new to this so I really appreciate all of the tips and advice! Will the fusible just kind of act like glue and hold the fabric down? I'm not really familiar with it....

I hven't read through the whole thread so don't know what the others suggested. I had this problem once and someone suggested that when I put my two pieces of material together to start sewing my 1/4' seam and I make sure that I can see my botton material. Not by much but see it so that it isn't slipping under the top material. I do that now and it works very well.

And IF the fabric seems to be likely to fray more, you could treat the edges with "Fray-Check" before restitching them.

I have had this same problem with a flannel baby quilt. Although I purchased the fabric at a reputable quilting store I did note that the weave of the fabric was quite loose, and should have known better than to just do a 1/4 inch seam allowance. I have learned my lesson and make sure that the weave of the fabrics I use is a good tight weave.

For mine there was no solution, but I sewed beside each and every seam and and he dragged it around till it fell apart. I think it was the fabric, not the quilter which caused the problem.

Congratulations on the completion of your first quilt. Sorry it didn't hold up really well. Looks very pretty.

amh