I want my roommate to let me keep a pet that I saved
What will you do if she doesn't allow it?
I'll tell her that I've decided to keep the pet, and scream at her if she refuses to give me her consent.
If you have a roommate you need to take their needs into account before you make decisions. Not all people are ok with pets and since you had no pets when you made the deal to live together, you need to agree on whether or not a pet is allowed now.
My pet is dying and needs a place to live.
I appreciate your concern for this animal, and I can understand why you want to keep it. However, the fact is that you are sharing a living space, and having a pet will be a big responsibility for both of you. If your roommate can not or will not allow this, then you will need to respect that decision and either give the animal up for adoption, or take it to another home.