It honestly sounds like kidney failure. Without, you know, being a vet actually examining your cat.
You need to find a way to take your cat to the vet for that sooner rather than later. Bad teeth won't make her throw up. Kidney failure will.
Regular treatments of subcutaneous fluids will flush her system and could give her extra years if this is acted on quickly. But that would mean convincing your parents to buy the needles, the bag of saline solution, etc. Most vets won't charge you a lot though. It is, however, very easy to do, I've done it on one of my cats that is actually rather unhinged (her mother's owners put lsd in her mother's water when she was pregnant) Admittedly, I had to trap her in a cage with a door on the top to kind of manage it, but any more agreeable cat will just let you do it.
You will need bloodwork to check up on her kidneys.
If she is having this and there is no option to deliver any treatment, I hate to say this, but that is consigning her to a slow death via wasting away and constant nausea.
Without a vet doing tests it could be anything though. But kidney failure is common in older cats.
Alternately, you could probably get the stuff for the fluids online and watch some youtube videos on how to give them. I would do it once or twice a day, probably once, and see if she starts to recover.
One worry about excess fluids this way is it thins the blood and makes the heart pump harder so if they have a weak heart, it can be an issue. I have never had this be an issue, personally.
I looked on Amazon but didn't see the needles (12 gauge iirc) or the bag of saline solution for sale. I believe the dosage would probably be 100mg. That's one line on the bag. You could probably hunt these down somewhere.
The needle is injected under the skin (not in a vein) around the shoulder blades. You pinch up on the skin and slide the needle in, then make sure you didn't puncture the other side or anyway. The fluids will create a large bump for a bit on your cats back while they are processed into her system.
Unfortunately, only a vet can tell you what is really going on.
Personally, I always used the "you are monstrous people and you neglect animals just like you've neglected me as a child and now you are failing me once again." line on my parents. They were bad parents, but I could guilt trip them well enough.