For me cutting all grains out of my diet has really helped in many different ways - and I never dreamed that I was sensitive to grains. There wasn't anything obvious, but cutting them out has made a world of difference. That is what worked for me. I certainly get plenty of carbs, just not from grains. I've come to really enjoy veggies with my breakfast and indeed it doesn't seem right without them any more.

Experiment and find what works for you!