I believe this was a standalone book, not a short story. I read it probably 10 to 15 years ago. It was a children's book. All I remember is one scene. I'm 99% sure the protagonist was male but it could possibly have been a girl.
This boy is a preteen or young teen, and has these mysterious itchy nubs suddenly start growing between his shoulderblades on his back. He does a lot of looking in the mirror to try to figure out what they are. Finally something pokes through and he tries to grab it and pull on it but is rewarded with searing pain as a result. Eventually feathery wings sprout. I think he tries to hide them from his family.
It doesn't seem to be "Black and Blue Magic," since the boy in that story used a potion to grow his wings, nor "Wings" by Aprilynne Pike or Bill Brittain.
Update: I've found the book "Wings" by E. D. Baker, which I have certainly read. It's about a girl who grows fairy wings out of her back after a lot of itching and soreness. I'm beginning to wonder if I just amalgamated several books into one and it doesn't really exist...