I'm really sorry that happened to you. If the person doing your wax is not careful to make you put on chap-stick around those sensitive areas, the wax will stick and pull off a few layers of skin.
In the future, make sure you put on a thick, wax like chap-stick and make sure the person waxing pulls your skin tight. If she is just pulling the strip you are going to get skin pulled off every time. She should be pulling the skin tight and should be pulling the strip close to your skin in an upward motion. She should not be yanking the strip away from you.
Anyway...yes, it is going to have a slight scab. For now while it is pink at night put chap-stick on it and keep it moist. In the morning be gentle when you are cleansing it but feel free to cover it with make-up. By morning it should be less sensitive and already starting to heal.
As it starts to scab over be careful not to pick at it or break the scab. Keep it really moisturized and then gently dab your make-up over it so you do not rub it and cause it to peel.
It will eventually get very dry one day and will be ready to come off. This is the point where if it is lifting off without any pulling at all, you can take it off.
Use to do waxing