My baby has a bad cough that won't let her sleep. I put vapor rub on her chest and have a cool mist humidifier on for her. Any suggestions?

Needs investigation. Chronic cough in a young child that is waking them up needs investigation. If it is not an infection, it could be an inhaled foreign body (i've seen toy parts, foods, etc). Also, high on the list is also environmental irritants such as smoke, dust, molds and then allergens causing the cough. One of the most frequent symptoms of early asthma in tots is that ongoing night cough!
Please stop the rub. Infants have sensitive airways and odors/good or bad can trigger more coughing. I never use vapor rubs before school age.
Depends. You don't state the age. Sleep cough does not necessarily indicate infection. Cough is a reflex and can be initiated by an irritable nercous system. If bottle fed try nutramigen. If older, remove all forms of sugar, all this assumes that your baby does not have fever or any indication of infection.