Developed eczema after new diet

Around August of last year I switched to an animal based diet to try and clear my acne, which worked. Lots of grass fed ground beef, steak, eggs, chicken, fruit, some veggies, rice, sweet potatoes, and some dairy. Around 2 months later in October I started getting these eczema like patches on my cheek which also led to a recurring impetigo infection. I’ve never had eczema or any skin issues except acne until I now. My cheeks are constantly red and irritated and they have never been like that before. This has been going on since October (past 6-7 months) I removed dairy, eggs, all vegetables, gluten/wheat almost 30 days ago. I have seen little to no results after removing potential food triggers. My question is could it be something environmental? I have 2 cats and 2 dogs, could I have suddenly become allergic to them? Or just something in the air? I went on vacation for 7 days to OBX in March and realized it was a lot better. I also went out of town for a day and it seemed better. It doesn’t make any sense to me why I would suddenly develop this after going on a diet that is supposed to heal eczema. Please help