I would def take her back for a second opinion - it is hard to tell from the picture on your profile. My whole family suffers from eczema, in particular my neice and my dd2 have suffered very badly. Saying that, eczema can effect different people very differently. My niece has never had it on her face, or on torso, just terribly on hands, feet, ankles, arms, wrists and behind knees. Whereas my dd2 gets in all over her face, neck, torso and back, arms legs, the lot really ! Her skin is always very dry and crusty and flaky, and her redness apears first in red spotty blotches, which she tears at. Summer makes it worse.
I hope your dd feels better soon, poor thing. My ds has never had any eczema, lucky boy, but I have taken him to doctors on a few occasions with weird spots, rashes. The doctor described them as allergic reactions, but said there was no way of knowing what to, ie could be a spider he ate, or a leaf in the garden etc!
good luck though