Hold old is your pup? Mine's 3 months old and the first week we had her, we didn't let anyone around her, then a friend of our's played a little too rough and she's been a rough-houser ever since. She'll bite at us, but she'll never draw blood, so that's a little concerning.
When you put her down, I'll leave her down till she settles down and stops crying. Like time out for a kid. If the kid's crying, you don't go get him/her out, you let them cry till they make themselves tired and calm.
As for the face biting, my little puppy does snap at my face when I put her on the stairs and play a little too rough with her. I tap her little butt and tell her NO! i can understand hands and feet, but the face is not a play area. If you play with them near your face you need to be very stern or else someone could get hurt.
If your puppy is very young she might have been taken away a little too early and might not know when too rough is, so keep on with the ouchs and stern no's.