@TheDemonzInside you would have been failing her if you kept her knowing you couldn't get her taken care of, this is the best thing you could have done and in doing so you show how much you care for them.
I had to rehome my 1-year-old dog recently due to not being able to give him the attention he needed because my baby was in the hospital, killed me to say good by but it was for his best to go to a home that could care for him properly, you didn't fail