Hi S.,
There are various organizations out there that do free spaying throughout the year. I am not sure where you are from but if you go to google or goodsearch and type in free spaying in (state you are from), a bunch of sites come up. You could also try www.petsandanimals.org. They have a spot on their site where you can select the state you live in and it will give you a list of organizations and fees. If you take her to a vet, they may also be able to recommend somewhere to get it done.
The urinating may not just be because she's not fixed. Our cat, who was spayed when she was young, also urinates all of the time. With her, it's behavior. We've had lots of tests done and nothing is wrong with her. Unfortunately, I don't know of a way to fix that. We haven't come up with anything. She gets lots of love and attention but still does it. I told my husband we are going to get cat diapers! LOL!
Good luck and I think it's great that you are exploring options and not getting rid of her. I know there are situations in which a pet must be removed from a home, but I've seen a lot of people (friends/family) simply get rid of them because they are no longer convenient. Again, good luck.
K.