I was allergic to eggs as a kid. I would get angry red bumps on my butt that really itched. My Mom figured out we (big bro and myself) were sensitive to eggs and took them out of our diet for the most part. As an adult, I’m pretty much able to eat eggs with impunity. I also voluntarily became a vegetarian throughout my teens from age 11 until I was 21 (then I wanted to eat a side of cow.) Now I’m 35 years old, I am dealing with my eczema/food sensitivities by doing an elimination diet (because the rash sucks.) So far, some things don’t bother me but normal hot dogs do. Basically what I’m saying is there is nothing really wrong with doing an elimination diet for a while to find out what does or does not bother her little body, and sometimes it might seem totally random. For me that was cherries, pomegranates, and beets. Go figure. But, for your little girl it might be something else.
As for healing: you might look into triphala. Its three herbs that are used in ayurvedic medicine to treat bowel problems. I used it to help grow my villi back after I threw an adverse reaction to antibiotics. Now, I’m ok in the villi dept (or so I thought, eczema be damned!).
GAPs might not help her. Not everyone feels good on that one.