*Disclaimer* This is my opinion based on research and our experience! It will probably rub people the wrong way or annoy some because they disagree, but this is my media ;)
The definition of allergy (as defined by dictionary.com) A damaging immune response by the body to a substance, esp. pollen, fur,
a particular food, or dust, to which it has become hypersensitive.
This means that ANYTHING can be an allergy. Allergy tests do nothing but tell you what a potential reaction to an object/food may be or the reaction to an object/food is at a particular time using a specific formula by the administrator to represent that object/food. It is by no means an exact science and results may vary depending on the doctor and the moment in time. A positive at least gives you a starting off point, but experimentation, elimination and challenge is the only real mode for an answer.
When you have an atopic condition your body has a "bucket" each allergen is a drop in that bucket and once it hits the brim ANYTHING can set off a reaction. This means that one day you could react to a mild allergy in a severe way and the next day you could eat/encounter it in excess and not show a thing. This makes life difficult to the person/people figuring out the allergies.
There are two theories in eczema....the skin barrier issue and the allergy issue. Well good news is they are both RIGHT! The Utopian treatment for eczema would be an allergist, dermatologist and natural practitioner. The skin barrier theory is that the body doesn't produce enough fillagrin which is imperative in proper skin barrier. But the very idea of this theory is an allergy!!! This root problem causes allergens to enter the body quicker and with more intensity.
It can not be said that allergies don't cause eczema unless in every case histamine levels were controlled, allergy tests were done and you have eliminated all processed foods from your diet. If diagnosed with multiple food allergies, it is likely that you are still consuming allergens if you have not seen a vast improvement. My daughter has been eating whole foods made at home for the last 9ish months and we have finally gotten her to a baseline with the realization that she is allergic to many real foods, but above all processed foods. You can be allergic to the process of production, you can also be allergic to food chemicals (MSG) which is in more than you know in various forms. She can eat apples, but not freeze dried apples!!! It is not possible to know your case of eczema is not allergy related until you have first worked toward gut healing (coming in part 2 1/2) and then scaled back to the foods that you are relatively certain are safe and given it a good 3 months or analyzed everything in your home that your child comes in contact with and experimented with changing it and the change in reactivity! Things you think are safe could be the very things flaring! In some cases it can take 2 days to flare from an allergen.
All this being said....a good allergist can help you to realize factors in the home, environments and diet that could be triggers. They are good guides into the journey to find causes to change instead of treating with topical steroids in an endless cycle of obsessive compulsive skin maintenance that we all get into! (Obviously this too is an integral part of treatment, but in my opinion is only a band aid).