Has she had her first distemper?
Could be a respiratory infection. Which is a big deal with cats this past year. You need to take her to your Vet and get her started on antibiotics. It's unusual for a kitten to live through something like that without the proper medical attention.
My cat always has this black stuff around his nose and I'm not sure what it is. Ive been thinking its boogers but could it be someone worse?