This is normal puppy behavior but should not be tolerated. I am going to suggest that yo sign her up for a puppy kindergarten training class. This will you to learn ways of dealing with other situations as well, and the pup will get the socialization skills it need to become a well rounded family dog.
Biting:Your pup has not yet learned what bite inhibition is. This is very common among young pups. The more you try to dissuade them they comes back even stronger, the more fuss you make the more excited they get. Sometimes even working themselves into a puppy frenzy. When pups are among their litter mates this is how they learn bite inhibition. Two pups engage in play, one pup gets too rough causing pain to the other pup, the hurt pup gives a yelp and walks away leaving the offending pup to wonder why play has ended. The more this happens the sooner the offending pup learns that it must not bite too hard or there is no play time with his siblings.With that being explained I want you to try that. When your pup bites, no matter how hard, yelp and walk away. Come back one minute later (no longer than one minute or the pup will have forgotten the whole episode) and repeat the process. I want everyone in the family to do this so the pup learns there is to be no biting at all. If you do this for a day to two days in a row the pup should soon subside.Another thing you could try during this training period is to buy some Granniks Bitter apple at the pet store and spray your hands. Pups do not usually like the smell or taste, (although there are always exceptions.) Once the pup smells or tastes this enough it will associate that smell with your skin and your hands won't be so inviting anymore.
When the pup’s biting has subsided remember to praise him for good behavior. Have him sit whenever he is near you and give him a treat, this will reinforce good behavior.
This is your pups way of getting your attention. If you yell at the pup while he is barking he thinks you are part of the pack and barking also, which reinforces his barking.
Teaching the pup the commands 'speak ' and 'quiet' will usually help with this. You will need to have handy a bowl of yummy treats that the dog does not usually get, like cheese chunks or hot dog pieces. To teach speak, continuously ask the dog to speak when he is already barking, then give him a yummy reward. When the pup is awaiting the next treat he will most likely look at you for one brief quiet moment, that is the time you want to say "quiet" and quickly treat him so he begins to understand what each command means. If you've asked for quiet and he barks, ignore him, this will have him wanting to figure out what to do to get the next treat.
I am going to direct you to a site on clicker training which is easy and fun, and can be done at home. I don not want you to skip any steps, print off a copy to keep for yourself in case you need to refer back to something. You will need a clicker which can be found in most pet stores for about three dollars or less.
I hope this helps,