I would suggest looking at the "Rules of Induction" on the Atkins site, as well as the "Acceptable Foods" list. Both strongly urge quite a lot of veggies. I wouldn't cut them completely out of your daily meal plan.

Atkins Center Rules of Induction

Atkins Center - Acceptable Foods for Induction

Eggs do have carbs: about 1/2 to 1 gram per egg. It helps to use something like FitDay or CalorieKing to track your foods each day to see how you're doing. It seems like extra work but it does pay off, especially when you stall, being able to track your intake.

I take blood pressure and acid reflux medicine, and have done fine following strict induction. I'm in my second week, and have already lost 15 pounds! One of my goals is to reduce or eliminate my daily prescriptions by the end of this year.