3 yrs old daughter, itchy and allergic to nuts & eggs

Hi,
I am really glad to find this site and forum, and I sincerely believe that I'll be able to find a cure for my daughter here.

She is itchy since she is born. The areas she is most itchy is at - inside of her elbows and inside of her knees. she starts itching from those two areas. I put Aquaphor and sometimes hydrocostisone 1% on her. As soon as those 2 areas are controlled she keeps on itching to other areas, and stops only when her whole body is covered with cream. this happens almost 3-4 times a day. Nights are worse, her affected areas starts to get warm up, and skin doesn't feel smooth any more, feels kind of like goose bumps. Another effected area is on her right hand below smallest finger, where it turns in a wound and it even starts bleeding.
Her growth -
She is 3 yrs 10 months old, but looks like 2 & half yrs old. Her height is so short. she is not too thin, and not too fat either, BMI seems normal according to her height.
Whenever I give her food, she starts itching her body. She doesn't seem to be much intersted in food.
Her pediatrician recommended allergy test at age 1, and we found out she is allergic to eggs, peanuts & all other nuts. Also, she started walking at 19 months of age.

condition -
skin itchy, burning, itches until bleeds, tearing, worsens at night.

let me know if you want more information about her.
Thanks in advance for your help.