What to do varies because human bodies, environment, and gut bacteria composition varies. It's more than diet. Inflammation due to lack of sleep, stress, or smoking is also a huge factor.

That said, the biggest factor for me was eliminating dairy. I used to drink more than a gallon of milk a week. I saw results after about two weeks of eliminating dairy. My dermatologist was shocked. She refused to believe there's any correlation between diet and eczema. Patches didn't start completely going away until I also eliminated wheat. They are basically gone when I regularly eat fermented foods, take a soil-based probiotic, and get good sleep.

You might want to try an elimination diet (starting with dairy, then wheat/gluten). If you want something more structured check out an auto-immune paleo protocol like Whole30. I wish that existed when I got started. Had to learn the hard and slow way on my own.