Well, it is a puppy phase, yes. But it is exacerbated by the fact that she left her mother and littermates too early. Puppies shouldn't be rehomed until they are an absolute minimum of 7 weeks old, and preferably 8 weeks. That is because the 6-8 week period is when puppies learn to be dogs (mothers are more than just a food source) - they learn how to play, how to accept discipline and
how to moderate their bite during this period.
Just to underline how important this developmental time is, animal welfare legislation in many parts of the world (including several US States) makes it
illegal to rehome a puppy prior to 8 weeks of age. Not sure what the law is in Canada...
Anyway. Since she was removed from her mother and littermates so early, your puppy has missed out on the education she'd have got from them. So you're going to have to compensate for that and teach her yourself. It's quite possible to do so, it just means that it will probably take a bit longer than if she'd already got a bit of education from her littermates. You're on the right track with squealing "ouch" and trying to redirect her. What her littermates would have done though, is squeal in pain and then retire away from her and refuse to play for a bit. So you should do likewise. Just squeal sharply, then turn away and ignore her for a little bit.
Not all puppies take no for an answer easily though

So if she really persists with the biting and continues to pounce upon you biting when you're trying to ignore her, then get up and leave the room for a minute or two. Shut the door so she can't follow. The message you're trying to send is that if she can't play nicely (ie. not bite hard) then you won't play at all. Soft biting/mouthing is OK, but as soon as any pressure goes into that bite, the game ends. She'll get the idea - how long it takes does vary, but if you're patient and consistent with your response, then she will eventually get it
