Oh my gosh... She looks bad. There is definately something wrong with her throat area. A vet would be able to open her mouth and check that out. I would ask for a culture as well. If it has nothing to do with the fuzzy then its an infection or severe irritation/swelling caused by something else. That snake really is too thin in my opinion. Even for a baby. But that aside. Are you going to take it to a vet or just wait it out? From the picture it looks like the fuzzy might be farther down the body and in the right place. Its hard to tell though. Did you watch the snake eat the mouse and watch it go down?
I dont know what else to say. They may not cost much to buy but these snakes can live 30 years if taken care of properly. I do hope you dont just wait it out because from the looks of that picture, she wont make it without some intervention..