Neuter scooters are great. Vet fees are ridiculous sometimes and those guys in the neuter scooter are vets! It is usually just a bit more up to you on after care. You pick up the cats really soon after the spay. So you need to do a little research before hand to know what to expect.
That is great if you can get into the next neuter scooter. Save up the money, show it to your mom, tell her you want to get the cat spayed and ask her to take you. You mom should be proud of you for showing responsibility and initiative. I used to take stray cats to the neuter scooter here too. I would just leave the traps out the night before and trap any cats I could and take them. I figured if they belong to someone, well lucky for them their cat is getting done for free. Anyways, occationally there was a female at the beginnings of pregnancy. They never charged me extra, but they sometimes can charge a little more. So keep saving after you get the amount they ask just in case.
It is so important to get it done. Try to keep her maybe in your bedroom until she can get spayed. She can actually be mated by multiple toms during one pregnancy. Usually all the kittens will be born at the same time, and some won't be ready. It can be tough on a female who is out loose. Those toms are aggressive when it comes to mating!