Hi, your physician has suggested the correct management and you should follow it, for your satisfaction you can go for complete pannel allergen test to get the list of all substance which are sensitive and then you should try to avoid all exposure to those allergen specially cold and dust, many times these allergy and asthmatic problems of children goes away with growth and you need to manage it till then , respiratory tract infection should not be neglected and proper antibiotics and antiallergic drug should be taken immediately.you should be in the toch of your physician for any aggravation of the symptoms , you can also consult a chest specialist for your satisfaction and if you want some other cource of drugs. take care.