My 4 year old has severe eczema and sees a dermatologist for it. Here is what we do: Limit the time in the bath, water seems to make it flare up. Right after bathing, apply Aquaphor or CeraVe lotion. For bad flare-ups (sounds like what your daughter has) we do whats called a "wet wrap therapy". Apply the medicated ointment generously to the affected area. Cover with warm, wet towel or washcloth and then cover with dry ones. Keep this on there for 20 minutes. After removing the washcloth, apply the Aquaphor or CeraVe. Do this for once or twice a day but for no longer than 5 days.
Could this be viral? Does she have any cold symptoms? Maybe something to ask the pedi about if she does. If it truley is eczema, keeping her skin hydrated and bathing with Aveno products could help.
Hope she gets better soon and that this doesn't turn into a cronic condition.