Meat making me sick?

I'm a meat eater. I mostly eat chicken and fish. I've noticed since I've become pregnant every time I eat it I get really sick. I can go a day and eat vegetables and fruit and be just fine but as soon as I eat meat I'm sick. Problem is I'm hungry so when I eat a full course meal it's because I've gone all day without having one. I've tried small portions and big portions it still makes me sick. Anybody else ever had this problem? Should I just cut meat out completely? Is that safe to do while being pregnant?