Asthma and cat allergy 5yrs old

Hi my daughter is almost 5 yrs and has just become allergic to cats in the last 6 months.
Since very young she was alway getting coughs almost every 6wks. She would cough at night in bed and it would almost alway result in her being sick everywhere, sometimse several times in the night. She would look puffy and red and get quite detressed. Finally one afternoon she came home from nursery with a bad cough and then went to sleep and tsrating wheezing quite badly, I did not realise it was an asthma attack ( I had questioneed doctors several times thinking she might have asthma) but took het to the doctors the nexty morning and was told she was having a moderate attack. So she went straight on a nebulizer and recovered after a short trip to hospital for further treatment and observation.
Since then I can see it when she is about to get wheezy, she gets dark circles, coughs a lot and talks in a laboured way. It does not seem to bother her too much so far. She also gets blocked noses and sneezing fits quite a lot and now has become allergic to cats. She used to have a hazelnut allergy but has over come it now. She is very sensitive and loving, but also has a very obstinate side to her character and used to get terrible tantrums. She's gemini and gets on with all ages and very sociable, however can be painfully shy when meeting other children who she dosen't know - but then with others gets on like a house on fire?! She had a very good memory and is quite quick and intelligent, grasps things very well. She has a very good appetite and used to eat endless amonuts of fruit when she was younger, not so much now as I'm stricter about mealtimes (realised she would keep eating) and often complains of sore tummy. I have to make sure she finishes her water often though as she rarely wants to drink anything. She also used to get eczema but much better now and we apply a natural cream twice a day which keeps it at bay. I would really like to cure her astham and allergy if poss. Can anyone suggest anything? Thank you!