Maybe a URI or something like kennel cough?
Several of the shelters we work with seem to have chronic upper respiratory infections going around and we regularly see dogs with snotty noses or coughing. Usually clears up on its own or with antibiotics. When they diagnosis KC they usually give us antibiotics and a decongestant.
She's probably been vaccinated but maybe with her lower immune system she picked up a bug somewhere?

She's probably been vaccinated but maybe with her lower immune system she picked up a bug somewhere?