Allergy testing should be your top priority
in the meantime
Dust mite encasements on all bedding and minimise all the fuzzy friends. Those that you have to keep put through a double wash and dry cycle. The dryer is essential, dont line dry. Take down bedroom curtains and if there are carpets in her bedroom, steam clean them and then vacuum with a hepa filter vacuum
Switch to super sensitive/hypoallergenic laundry detergent, soap, dryer sheets, literally anything that touches her skin needs to be fragrance free.
Stop using perfume yourself and throw away any airfresheners
If you have pets, you might have a really big problem, but for the meantime try and separate pets (and pets items) and child as much as possible.
once you have minimised all the potential environmental allergens you can, you can reintroduce one at a time to see if there is a flare.
You also need to look for food allergens, hence the pediatric allergist and allergen testing
Ask the GP about giving her antihistamines on a daily basis to try and reduce the allergic response and keep a close eye on the folds of skin behind her ears, knees and elbows for cracking skin that can get infected. She probably needs steroid creams to knock back the flare and then a good moisturising routine might work for maintenance.