My 1 month old baby has rash at her face. it's small but have covered her whole face even on her ears and head and eyes. her skin is reddish?

Baby acne: From your description and the area involved, sounds like baby acne. Baby has been exposed to your hormones for months. At birth, sudden withdrawal of these hormones. That causes glands to hyper secrete and sometimes plug the sebaceous glands....and proof.....baby acne c'x develops. It's likeky to get worse a few more weeks,then will gradually go away as glands get accustomed to new hormone levels

Atopic dermatitis: Atopic dermatitis (atopic eczema) is the most common chronic relapsing skin disease seen in infancy. Most often affecting face and scalp in infancy, and affected area is dry, scaly, and reddish in color. Intense itching leads to scratching. Keeping the affected area moist and application of low-potency steroid cream would provide relief.