This was my initial thought too. DS has asthma, and would be woken up with a night cough just like you describe. The Pulmicort works wonders with helping him sleep through the night.
We use Pulmicort, too, and DS had reflux and was on Zantac for that until a couple of months ago. We also find when he gets sick (and is woken up by congestion/coughing) using a nebulizer (with saline, or albuterol - by prescription from the pulmonologist) helps him breathe easier.
I would recommend consulting a pulmonologist for the coughing. They would probably be able to decide if it is asthma, and how best to handle it.
Once you are able to make her confortable at night, then you'll be able to tackle the other sleep-related issues (night-feeding, etc.) The Healthy Sleep Habits book is great!
GL!