Most common cause of cough
at night, disturbing the sleep is wheeze due to constriction of bronchi.
That's why your doctor has advised nebulisation.
And saturation can be normal in many non-severe wheezers. It has nothing to do with the decision to nebulise.
So please take her back to the Pediatrician
and get her nebulised. The Pediatrician may even prescribe a short course of steroids
as its almost 3 weeks of the illness now.
Also have her throat checked.
If the episodes are frequent, you may ask the Doctor for medicines to prevent such attacks like Montair/ Steroid inhalers.
Hope my answer helps you.