Yup. It's quite normal to have cravings almost constantly when you first quit. You are no longer feeding the beast.
You see, the insidious thing is, you think that having a smoke will ease the craving. When in fact, it is the cigarette itself that is CREATING the craving to begin with. It's a fact. That is their job. Not to soothe, but to create another craving that needs to be soothed. When you realize that insidious fact, it should make you angry. It was that little shift in my mind that turned me into a winner. I got angry, and thought "you little bastard! ('scuse language) You will NOT BEAT ME!!!!!!"