I would try another doctor. The medicine does indeed sound dangerous to me, and so does the cough. It would be good to know what she is allergic to, and how she could get relief without medicine.
A few safe things to do:
-get an air cleaner--But check Consumer Reports. Some of them do NOTHING, but some are REALLY good. I have an awesome one that I used when I had pneumonia because I knew there was mold, to which I am allergic, in our building's ventilation system.
-Wash her bedding in HOT water often. If you can, hang it in the sun. This will help reduce dust mite activity. My ex-husband, who was horribly allergic to dust, used a new pillowcase every night. Remove fuzzy rugs from her room if possible. Go to a bare floor.
-Try a humidifier. If she is allergic to dust mites or mold, though, this might make the allergy problem worse!!! So be careful.
-turn down your heat at night. The cool air might help reduce inflammation, and the heating system will not be blowing dust and mold. If you have the opposite problem and the room is too cold for her, get some kind of heater for the room that does not blow air (like one of those radiant oil heaters).
--check to see if she is being exposed to diesel fumes. I have heard that the rise of asthma in kids might be linked to the use of diesel in school buses. Of course, she's a little young for school, but some kids are in early these days!
And maybe not safe:
--She might have asthma. Asthma in adults apparently responds well to wild cherry bark tea. But I have never heard if this is safe for children. Check with a doctor!!!!!