hey!
the list could be quite long in terms of testing and it geatly deends on her health history. I would have your doctor send her for any testing he feels is appropriate. A few tests i encourage my clients with eczema ot look into are: food sensitivity testing, mold testing, crp, il6, wbc, neutrophils, iron, 25-hydroxy d3 and 25 dihydroxy d3, and stool testing (although not always super accurate as pathogens can create biofilms which prevents them from being visible in stool) but is still a good idea.
hope this helps 🙂