While I have no technical experience with these issues, I have done a LOT of research on Miracle II soaps & neutralizer.
If you'll go to Google, type in Miracle II, and start reading the testimonials, you will find that thousands of people have been totally cured or received fantastic relief from eczema, psoriasis, dermatitis...and ESPECIALLY the itching associated with them...simply by bathing in the soap & neutralizer fluid.
I have used it for years, and find it's like an "ER in a bottle". The soap, gel & fluid are totally safe and without any chemicals or toxins. It can be purchased on eBay, hundreds of health related sites on the internet and there are thousands of distributors world-wide.
From what I've read, it seems your lil' one would achieve AT LEAST a 50% reduction in symptoms immediately! Of all the natural/health products I've used in the past 40 years, this is one I absolutely wouldn't be without! If ever you trusted any piece of advice from any stranger, PLEASE trust this advice...I am SURE your daughter will see an immediate reduction in symptoms (especially the itching) before she even gets out of her first bath (she might even enjoy her bath, as the neutralizer zaps all toxins and irritants in the water :)