More likely you're feeling dizzy because you're not eating nearly enough or enough of the right things and that's not good.
Cutting out sugar is a great start, but don't cut everything else out in the process. You need to get used to eating a lot more healthy than you are if you mean to maintain this as a lifestyle! You need veggies! The majority of your carbs should be coming from veggies, not coffee and low carb shakes. Go easy on the shakes and the heavily processed meats and salty foods. Eat real food with solid nutrition to it! From the looks of it, you also need a lot more water (I didn't see any mentioned) and probably more protein as well.
You may want to go back and re-read the chapter on induction. I don't think Dr. Atkins meant anyone to follow induction eating as you are.