We adopted a 3 month old "blend" from the shelter and took her to the vet for shots including nasal kennel cough. The next day she was listless, could barely move and had a nasal and conjunctival discharge. She too was declared to have distemper. We elected to treated her with antibiotics as I thought she might have reacted to the nasal kennel cough vaccine. She's now over 6 years old (and can be quite a pain in the butt!).
It's very possible that she DOES have distemper, but it's really worth trying to treat her. I wish you (and her)the best as I know that it's very stressful. I know it was a tough few months for us but they're worth it.