Your post raises a number of interesting points, but they all come back to a central reality: your diet is very limited. I think you might have more success furthering your fitness and health goals if you work on broadening your range of healthy food items, rather than do an induction type of thing, where you will be concentrating on limiting food groups.

The other thing that jumps out is that you feel sick in the morning, and that dicatates your breakfast choice, which is mediocre at best, and as we all know, what you eat for breakfast shapes what you eat for the rest of the day.

So first off, I would see if there is any way you can get yourself into eating a better breakfast....that may mean addressing why you feel ill in the morning, that may mean just setting things up so you can eat (like getting more sleep, getting up earlier, or not drinking black coffee first thing, finding a breakfast that agrees with your tummy, or having a well rounded pre-bedtime snack).

I think you might get a big boost here if you consult with a nutritionist, or a GP/nurse/naturopath with an interest in nutritional counselling.

Meanwhile, work at incorporating more fresh fruits, veggies, fibre sources and what they call "whole foods"...foods that are, as far as possible, unrefined and unprocessed. We can all help with menu suggestions there.