hi there...in all honesty, any baby i have ever known (all my nieces,kids i ever babysat for, my own daughter, etc) has had a rash on their face or body at some point within months after being born. my daughter had this for 2-3 months, as well...
what generally happens, the baby absorbs toxins from the mother's body while in the womb-it's a natural occurrence. these toxins can express itself through a rash on teh body.
the first 4 months are of the baby's life is considered the 4th trimester-when the baby's digestive system and such are still developing (hence a lot of babies get colic too!) this time of the baby's life, their intestines are starting to work, they are absorbing foods that they've never had...if it's breastmilk-then they need to get used to what the mother is eating (which is why mom's who breastfeed need to stay away from certain foods) and if it's formula, then their systems have to get used to the soy, sugars, etc. the rash is usually the baby's way of releasing and working with what he/she absorbed from the mother's womb, in addition to what their newbie intestines are working with. are you feeding her solids yet? stay away from sugars as much as possible...unless they are natural forming-like in sweet potatoes, fruits, etc.
probiotics are an excellent way to decrease/diminsh baby eczema. they even suggest the mom eating acidophillus while the baby is in the womb to decrease the chances of the baby having eczema.
maybe try rubbing some greek yogurt on the baby's skin? (greek yogurt does not have added sugars in it; not yogurt with sugars in it, as this might irritate your baby's skin) as i said above, i'm not sure if you're feeding her solids yet, but you can try giving her a bit of the greek yogurt (you can get this at greenlife, earthfare, ingles also) to eat, as well. cooling cucumbers on her face might help too, if it is 'burning' or irritating your baby. aloe, as well.
i would also use an all natural soap that is geared for baby's skin-like burts bees or aubrey organics. i know these tend to be pricier-but there are a lot of synthetics in regular soaps (even though they say that dove is for sensitive skin) that tend to irritate the skin and baby's skin is soooooo sensitive, as you can see.
if you need anything other info, i'd be happy to help!
i'm a mama of an 8 mo. old girl and a licensed acupuncturist, here in asheville...