Christine, Zoe is NOT vicious. He is a puppy. He is teething. This is very normal behavior.
I expect he considers your "no" to be a bark which - to him - means you're playing the game, too.
Try this. Keep lots of chew toys and bones nearby (in every room). Anytime he bites something inappropriate, substitute something he can have. If he bites you hard enough to hurt, yelp loudly and immediately break eye contact and turn your body away from him. If he continues, walk away from him and ignore him for a minute or two. After that time, all is forgiven. You will have to repeat a bazillion times but he WILL get it!
Remember the important thing for him to learn is that biting you means immediate loss of your attention. Biting pup = invisible pup. Not biting pup = the best little doggie in the whole wide world!
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