Thanks for consulting at Healthcare Magic.
Cough, cold, runny nose rash etc. suggest possibility of viral infection or
allergy.
As your daughter is already diagnosed to have
asthma, probably complaints of your daughter are due to allergy.
Episodes of cough, runny nose, chest congestion occur due to exposure to allergens.
You will need to identify what is triggering such episodes. It may be allergens like pollens, dust, mite etc, Some times chemicals like perfumes, mosquito repellents etc.
Adequate treatment may not be as effective if exposure to allergens is continued.
Ask your doctor for medications like Citrizine, Xylomist Drops, Nembulisation​ with
Budecort and
Levolin,
Montelukast etc.
If no relief consult pediatric pulmonologist for further evaluation.