6 things appear as white patches on the skin in kids
1) Sun allergy…. normally seen as roundish rarely rough coin shaped patches on the sunexposed areas of the body.
2) Pityriasis alba… Looks like whitish coin shaped lesion. normally doesnt itich.
3) Tinea versicolor…. fungal infection due to excessive sweating or moisture. normally seen on the trunk but can happen on the face also. Not itchy.
4) Atopic eczema….. kind of dry eczema, can be very itchy and very rough to touch.
5) Naevus depigmentosus…. A birthmark which has no colour… can develop at any age
6) vitiligo….. leucoderma… an autoimmune condition where the cells producing colour are destroyed resulting in a white patch.

These are the commonest causes of white patches. I suggest meet a dermatologist who would help to diagnose what it is. To start with some treatment at home. Apply a moisturizer 2 3 times a day, apply a sunscreen. Amild cortisone cream would help in all the conditions except the fungal infection… which would worsen it and the birthmark which would remain unaffected

doesn’t sound like eczema. eczema has itching with moist or dry lesions.
sounds like a condition called vitiligo, where white spots or areas form from lack of pigment cells. Take her to her pediatrician, or a dermatologist, they can better determine what those white patches are and suggest treatment.