Hi E.,
Most skin problems are systemic and come from lack of nutrition in the body. They exhibit on the outside. Yes, outward remedies may help, NOT vaseline, baby powder or lotions, but tea tree oil to dry and heal or something like witch hazel.
Look at your child's diet. If you believe her to be eating well then it is possible that the nutrition is not actually being absorbed. If she's not eating well, change her diet immediately. This is common today and is caused and is causing digestive problems. Digestive problems, like Celiac's disease mentioned before, show themselves outwardly.
Chiropractic care can help with the absorption as well as putting her on an absorbable multivitamin. Avoid Flintstones and the wannabe Flintstones, they are completely sugar and do more harm than good. If you need recommendations, I'll be glad to help.
God bless and feel free to ask more if you like.
M.