Blood tests are ok, but, there is a finite limit on what they test. Also, someone who is very good at muscle testing can help determine whether your body is digesting food properly... that is, it can be much broader than specific food allergies . I found it very helpful.
re the Antibiotics , sure there is a price to pay, but it sounds like you had limited options. No doubt the anti-biotics disturbed bowel flora, which takes time to heal. I've dealt with eczema on and off all my life (and am still working on it). I wish I could tell you that there is a simple formula that can work, but, people's results seem to vary with different approaches. for some, eating really healthy food for awhile will be enough, others, like me (who used steroids ect for years and years) have a harder time. Its good that you are helping your daughter face the issue while she is young, before it is suppressed for years. I wish my parents knew the dangers of medication.... but I digress.
Healthy diet, sunlight, avoiding Sugar and process foods, avoiding medications.... we did BRT (body restoration technique) and homeopathy for our son rather than drugs. He has been clear of eczema for several months now, but gets hives on occaison. He has not developed breathing allergies or asthma which tends to happen to eczema kids. Frankly I attribute this to the fact that we did not suppress his immune system through medication.