I dunno about injecting my cat with stuff. Sounds like vet territory.
As for putting the cat down, she still wants to eat a lot and purrs and lays on me a lot, so it doesn't appear she's in a ton of pain if you ask me. I don't think we're there yet. She still jumps and stuff.
Besides, no vet saying anything yet.
Trust me, and look at the link. You're not injecting anything into your cat's veins, it's just under the skin. It' sterile saline solution. Basically, if this is what it is, your cat's kidneys are failing. She is unable to process the toxic stuff that comes with eating. So she won't eat and will feel very nauseous.
Some people that are into body modification inject themselves with this saline stuff for fun. It's harmless, the body absorbs it and it won't do anything but hydrate you.
The subcut fluids flush her system.
Even if that isn't the problem, this would not hurt your cat as long as you use sterile needles and the proper bags. It's easy as all hell.
Your last line: did your parents agree to let you take her to the vet, then? That would be optimal.
Anyway, you can definitely find youtube videos for delivering subcutaneous fluids, which will clarify everything. I've done it for four different cats. Actually five... Sometimes for kidneys, sometimes because they were sick and were not getting enough fluids, and a couple times when the cat was dying and we were just giving it a week to see if there was an improvement (and they weren't drinking on their own.)
But now you say she's eating? Is she still vomiting?
If it is kidney trouble, letting it go and doing nothing is a long, drawn out death. The fluids can extend a cat's life, if regularly given, for a few years. The first cat I had that I did this with lived for another two years, she was twenty or twenty-one when she died and she was in good spirits for some time until the end. No fluids mean the toxins continue to build up though. There is no extension of life.
TBH I wouldn't take advice I got on the internet about my cat. Make your parents feel like shit about the whole thing. (Unless you think that will make them sick of it and they'll put her down to be done with it.)
When my cat Missy, the one that lived to twenty-one, first got sick my mom said she was just dying and she was comfortable. I think she wanted her to stumble off and die somewhere else. I kept trying to feed her though, but I didn't push to go to the vet for some reason I can't figure out. I think I kind of believed my mom that she was going out peacefully.
A friend of mine had arby's and he tried feeding her roast beef from it and she ate some and we were very excited, and I realized that she wasn't dying peacefully, that she very much wanted to live.
When I took her to the vet they said that it is very painful and she was starving to death and feeling nauseous the whole time. Cats are just so stoic about everything it can be hard to tell. (I had a cat with a detached retina that was causing an ulcer inside her eye that acted perfectly fine, and that had to be horrible.) This was a pricey vet though they were good. They said they could take care of her for $400 or so, deliver the fluids etc and watch her, or I could do it for much cheaper (though my personal vet charges way less for the fluids than they did, like $20. I can't remember what they charged but it was ridiculous.)
I called my dad, who refused to ever refer to the cat as anything but "that cat", and who had just bought a new jeep and was paying for my mom to get dentistry work done, and he didn't want to pay for any of it. He called them back and asked how much it would be to put her to sleep. He was like "If I say no you're going to think I'm an ogre" which I clarified that yes I would because he was, in fact, acting like a monster.
Anyway, he paid for the fluids and I stayed at his house for a few weeks giving her anti-nausea meds once she would actually eat and delivering fluids to her. (she fought the whole time, a friend stayed there with me because it took two people to do it and there was no way to feed her pills directly. She'd snap her own neck before she'd let you do it.)
She lived two more years and I only gave her fluids while she was not eating and feeling nauseous. Had I been able to continuously treat her she might have lived longer.
Also, don't get another animal, don't let your parents get one. If they aren't willing to pay for basic veterinary care, it is best not to have any.