nine month old babies often suffer at this age with above complaints in this season.. it resembles flu but in these infants often it is termed bronchiolitis
caused by some virus.
Runny nose and fever is best tackled by medicines that contain paracetamol
.. often doctors prescribe medicines like say sinarest, maxtra p, solvin cold, flucold etc.
is needed only if cough lasts 3 days beyond fever or chest gets wheezy or distressed. One important issue to be ruled out is possibility of pneumonia
Often when she vomits with cough its likely that either the throat is inflamed or child has airway narrowing.. that responds to asthalin nebulizations. you may read more of cough cold at www.breathingdiary.com
I hope this answers your query.. for a detailed advice please take advantage of paid service.