I am sorry about your situations. Both about you becoming homeless and about having to hand out your little loved one. It would break my heart.
My first two parrotlets were Bo and Jules. We got them from a over extended bird woman that had previously gotten them from others that give them up. One or the other of them may even have been abused before she got them. They were a bit sad at first but got over it quick enough. Our little ones are smart and can handle things much better than most of us owners think they can.
But if you get her to a new home where she will be loved and treated well, become a flock then she will be fine. She may even remember you if she sees you again. I know my Jules did for her previous owner. She just viewed her as a flock member that was away for a while.
In the end your responsibility is to do what is best for yourself and for her. Just be sure she will go to a good family that will treat her right.