Coughing is often the biggest symptom in asthmatic attacks, and asthma can be triggered even in non-allergic people by a viral or bacterial infection. Ask me how I know--after a visit to the ER in a foreign country for my first acute ashma attack.
The treatment for this involves a "rescue inhaler" (probably the 'blue one' your daughter is using several times a day) but ALSO a steroid inhaler for long term control, plus steroid pills for a couple of weeks, and an antibiotic if the doctors suspect bacterial infection.
Since your daughter is being treated for asthma, it would be a good idea for you to check out the asthma forum here:
http://www.medhelp.org/search?utf8=%26%23x2713%3B&query=2011+asthma