I finally figured out what she is! She is a Crimson-wing Finch. Unfortunately they are only native to Pakistan and Morocco so bringing her to a rehab is useless. I'm going to keep her and make it my duty to find her a mate. From what I understand they aren't really popular in the pet trade but are cage birds in certain areas. I found a breeder online but they are relatively expensive ($160 a pair+shipping) so I'm going to have to wait for now.