Not sure exactly what you mean. Would you use heat n bond to secure the label? You could use a strip of seam a seam to hold down each edge to secure the label.
You can also use a stabilizer or starch to stiffen the label fabric. Not sure why the label balloons out.
I make my labels on the embroidery machine. They are doubled in size so I can fold RST and stitch to create a pocket. Turn right side out. The top of the label is folded so no raw wedges there. There is one side seam. The two raw edges are sewn into a corner of the label. Then covered with the binding.
There are only two edges left to stitch onto the quilt. The top edge and the side where it was seamed together. I pin the label onto the quilt to hold it in place while doing the final stitching.
The reason I double fold the label is to have some extra fabric in case of tears or tatters. Matching fabric is already in the quilt. Hope that helps!