Just speaking from my own experience, I have asthma and was diagnosed as a young child. My asthma was brought on when I got out of breath- ran around or moved too much. I had a steroid preventer and a blue salbutamol inhaler. I got by on my steroid one and rarely used the blue one. Then I ran out of my steroid one, took just the blue one for a while, and once i went back on the steroid one, I needed the blue one too. ie- I had become reliant on it. I am a bit wary of giving kids salbutamol when they may not be asthmatic. The coughing at night thing sounds exactly like this horrid virus which has been going around. It is an "itchy" cough, made worse by lying down. As a virus, it doesn't respond to ventolin or antibiotics.
Without a doubt though, my asthma was caused by me eating and drinking dairy products as a baby/kid. I also had eczema and as an adult have various auto immune things, which I feel are linked. All of this is only my experience though; does your baby have dairy?