This story and the ones like it break my heart. I am usually 100% against lying but in this case I think you should 100% lie. After you have had her for the couple days as you mentioned I think you should make up a story and say you had friends over during that time and they fell in love and want to adopt her! Then I think you should either keep her if that fits in with your family and what you are able to do or if not try to find her a home.
I'm so sorry, I really hope this works out and everything is okay.