From what you have shared, it sounds like maybe scarring has caused a narrowing of your baby's esophagus and that they want to be a procedure that stretches the esophageal walls.
Like said before, I would talk to your vet about this procedure - risks, benefits, what to expect, what is the prognosis with and without the procedure. The vet should be going over all of this with you personally before he/she performs a procedure on your pet.
Please be careful in the future with animal bones of any kind. Your dog is still young, and I would not get it in the habit of eating ppl food. It really is not good for the dog. They do not digest the way we do. They are not capable of handling the fried, spicy, fatty foods we are. Bones can not only lodge, but they can perforate the intestines - which would need surgery to repair. I know your pup looks at you with those puppy eyes, but she does not understand the dangers of what she is asking you for.
Please let us know how she is doing. She is such a cutie in your avatar!