As frustrating and hopeless as your daughter's case seems, I still believe that she can make a full recovery and experience eczema free skin. The understandable dilemma that you face is your need to bring your daughter instant relief from her suffering. Unfortunately those things that bring instant relief (benadryl, cortisone creams, & prednisone) further weaken the immune system and create the viscious cycle that you have. From personal experience, I can tell you that prednisone is extreme. It is a very serious drug and you need to make the physician aware of your daughter's liver condition should you decide to take that route. The focus has been on foods as your daughter's major eczema irritant; however, I strongly believe that the medications have been your daughter's biggest threat to healing. This is why there is a vicious cycle; because the medications that promoted the longterm suffering are the medications that you now need to end the immediate suffering.
I know that you've been given a long list of food allergens for your daughter. I don't believe that this list is indicative of a lifetime condition. It makes sense that a very weakened or compromised immune system would display a vulnerability to a multitude of allergens. Although you've tried to make the switch to less damaging medications, her body would still contain the remnants of those medicines in her system which should also be considered when doing allergy testing.
I believe that a major turn around in your daughter's health is going to come from the inside, out. I believe that this will happen with something that most people find irrelevant and insignificant to her healing, her nutrition. Like I said, a lot of focus is placed on what she can't eat; however, there remains a significant hope in what she can eat. Dark green leafy vegetables which contain both the fiber and the beta carotene that her body needs to promote the healing will be key. I would focus on a daily consumption of these vegetables. In addition, squash, carrots, sweet potatoes, cantaloupe, and romaine and green lettuce are also good sources of beta carotene. I know that you've focused on getting these nutrients through vitamin supplements; however, it is even more significant that these nutrients be consumed through whole foods. The green vegetables were daily staples in my nieces' diets; especially in their infancy/toddler ages. In addition, oatmeal and garlic & chicken soup were also major staples. In addition to that, drinking plenty of water was also necessary. These things seem insignificant to most people; however, these things are the body's true medicine.
Your physician has suggested prednisone and stated that this was the alternative that would promote healing. What will happen is that the symptoms will be suppressed to give the appearance of healing and her itch will probably cease immediately. Keep in mind however, that this is a short term drug with serious side effects. If you need the short term relief (simply cannot take it anymore), then proceed with caution and make sure that you address her nutritional needs (with the foods mentioned above) in the process.
If there was a test that I would have suggested you conduct for your daughter, it would have been the metal/mercury test. Chelating will probably prove to be very beneficial to your daughter's healing.
Don't feel condemned for your daughter's current condition; you got caught up in a cycle of suffering because you (rightfully so) trusted the physicians to have your child's best interest in mind. My warning cry to the parents of eczema babies was to avoid the very thing that you are now suffering with your daughter. This was why I was adamant that my brother not take this route (conventional medicine for eczema treatment) when it came to my nieces. I knew that they would have ended up in the same predicament that you now face. Nonetheless, I still have a great deal of hope for your daughter. The process for healing that I would suggest would probably mean two weeks of more suffering until the healing process was complete. I can't ask you to do that and that becomes my dilemma. Your child has been suffering for 2 1/2 years too long and I can't ask you to prolong it; because you need the suffering to end today.
The most important medicine for your daughter out of all the medicines are the whole foods mentioned above that contain the fiber and beta carotene needed to promote her good digestive health and immune health. The two are directly related. Her poor digestive health is promoting poor immune health. Though foods have been tested as her major allergens; it's going to take the healing nutrients found in foods to restore her health.