That's good news that she's came around so well and so quickly
As far as her chewing on your fingers etc, that's ok and can be allowed as they tend to do this when playing with you and they usually do this only to someone they really like
The part about the one person bird agression thing, the only real way to stop this is to get your family involved with her and interacting with her on a regular basis, then it can still take some time. Part of this problem is that the bird has bonded with you and may see you as her mate. When this happens, she's going to fend off anyone who tries to pet her, pick her up, or if someone just gets too close to her. It can range from anything from a warning nip or growling to a nasty bite. The bird may also attack anyone that gets too close to you or gives you a hug or affection, the same way they would fend off any competition in the wild. This is more common with a mature male bird, but the females can have their fits too. To fix this you would need to limit the amount of affection you give your bird and pay attention to her body language, discouraging any signs of mating behavior, then working more on socializing her with as many people as possible.
The other part is where the bird just isn't socialized and only trusts you but nobody else, this is most likely the case. What happens here is that the bird won't let anyone else get close to her or she'll fly off, or if you got her and someone tries to pet her she'll growl and maybe strike at this person. She will bite if this person pushes the issue, but usually only after warning them to back off, and attacking for no reason is uncommon, the bird will keep to herself for the most part when out of the cage and others are in the room, she'll fly off if anyone gets too close and won't do anything to anyone unless cornered. She may protect her territory like her cage or the room she hangs out in, but for the most part she just won't tolerate others touching or petting her. This can be fixed by working with her socialization skills and by introducing her to anyone who comes to the house. People should be told which commands you use when stepping her up, and know to stay calm and not act scared of her. If you're using the "gentle beak" or "be gentle" commands, whoever else is going to handle her should know these commands and the bird will usually obey.
Just keep working with her and keep building up a strong bond with her but try to get the rest of your family involved with her by stepping her up, letting her hang out on their shoulders, or hand her treats etc to help her tolerate them better. You can also bring friends over to help you work with her as well.