This is very similar to me. My brother and I also have EC but his is not as bad as mine and he also has wheat allergies, possibly celiac's disease. I went to a famous Chinese doctor in China in January and he said it was food allergies and intestinal problems causing EC on my lips. He gave me lots of medicine, stuff to put on my lips, diet plan, and other stuff but it didn't work.
I am currently doing the moisturize method (I just finished a semester of school and had to peel the skin off every week) and people here were talking about Imuran and someone said something about it being for intestine/bowel problems or something and so I want to try it but I am waiting for more information first... I used to have diarrhea like everyday but I stopped eating gluten and don't have as much diarrhea anymore, but still have EC.