First off i would like to say this is why people shouldnt just get a dog because your other one passed away, especially from a shelter, if you want to get a dog from a shelter, you should go there, look at all the dogs and find one that fits your family, dont get a dog because you feel bad for it, because sometimes that can be the worst thing for it.
Even if the dog does have pitbull in it that has NOTHING to do with the way it is acting, obviously you need to teach her some manners, if she was about to be put down then you should have expected some quirks, not some perfect already trained dog to replace yours. I really do respect that you saved this dog but it seems like its gonna end up in the same place it started if you dont correct these things.
I would also suggest taking her to obedience classes and LOTS of exercise. If my dog hasnt been taken out for a 2 hour walk then she can definatly be a handful.
Shock collars are not the answer to your problem i can promise you that, its just going to make you and your dog alot more annoyed then neccisary. Plus shes just a puppy, all shes looking for is routines, rules and boundaries.
I would suggest contacting a professional asap and getting this sorted out, they would be able to help more then the internet would.
I wish you and your pup the best of luck.