Thanks for query,
Your daughter seems to have allergic bronchiolitis
There should be some allergyfrom inner side out from outer side.
As there is h/o eczema
in the past so this may be due to eczema.
Find out the cause of allergens and avoid them.
Go for blood test
to rule out bacterial.viral or allergy.
Give anti allergy syrup,cough
suppressant and if require go for antibiotic medicines.
Consult your doctor and get investigations done.
Ok and bye.