K.H.
It is ok to wait it out. She will be fine. I and my ped are firm believers in waiting it out. They can't giver her meds for something she doesn't have yet. It will only help build up her immunity by letting her body fight it off. It is necessary in some cases to need antibiotics but the reason why we are having issues with these superbugs is because over the decades doctors have over prescribed antibiotics.
Her coughing all night is definitely frustrating but that comes with having kiddos:)