You should still be in ketosis if you did not eat carbs.
Atkins is a ketosis diet, and you eat WAY more protein and less veggies on that diet than this one, so don't worry about that.
You get a 1/4 cup milk? I was told 1 ounce per day, which is only 2 Tblsp, not 1/4 cup. And no, no cheese is allowed. Those are the rules.
On the other hand, I will admit to using 1/4 oz very finely shredded cheese on my omelets, but die-hard IP'ers will say NO NO NO. Cheese will not put you out of ketosis, but it's very high fat, which is why it's not allowed on IP.