I recommend giving the diet the whole time suggested. It does take time for things to cycle through your system. Dairy is particularly pernicious--people react up to a month after consuming dairy.
Have you looked into other causes of skin problems (I mean, in addition to DH)? It might be helpful to keep a diary of what you are eating and when you have flare ups. I do this in my planner (I use the Bullet Journal system which allows you to create your own planner out of any notebook you have).
FWIW: I react to eggs themselves with eczema (believe me, I get the funny in this). This means I can't eat a plate of eggs. I can eat them sparingly in baked items (where it's like 2 eggs for a whole cake and therefore the amount I eat per slice is quite small).
I also have a thing called Oral Allergy Syndrome (also known as Food Pollen Syndrome). It's where you have environmental allergies (to things like grasses, ragweed, and tree pollen) and then your body mounts a reaction to raw fruits, veggies, nuts, and certain spices that have the same pollen protein signature (it is only caused by things from the plant kingdom). Often the reaction is itchy mouth or other digestive reactions. Or it can cause more serious reactions. Less common but still possible, it can cause itchiness in the skin. The weird thing about OAS is that cooking food often breaks down the pollen proteins, allowing me to eat the thing. Sometimes the protein is too strong and even extreme cooking doesn't denature it. The important thing about OAS is that it is not a food allergy--so food allergy testing doesn't help diagnose it. The best diagnosis is to see what environmental pollens you are allergic to and then correlate those with the foods that you eat raw. Please be aware that even a lot of allergists don't know about this. Here's an article I wrote about it to help others understand the basics: http://www.artofglutenfreebaking.com/2013/04/oral-allergy-syndrome-oas-or-food-pollen-allergy/
The main issue with OAS is that I can't eat most fruits, veggies, and nuts raw. It's a PITA but it's not that bad once you get used to it.
Also, have you looked into Mast Cell Activation Syndrome (MCAS)? It also has a strong skin component. Here's more info: https://tmsforacure.org/
Again, hang in there.