Cat has liver cancer and is hard to take care of but in very good mood

My cat has had a terrible mouth infection, full of infections and ulcers. She stopped eating and dropped A LOT of weight so I took her to the vet. The vet said her liver values were very high (they've been moderately high in the past, but this was triple what they had been) but maybe antibiotics would help if she had a liver infection and mouth infection.

I gave her the antibiotics and she began eating again, and actually gained a little weight. The problem is how she eats. She will now only eat filets or bits of wet food, not pate. And she can only eat a spoonful every half hour or so. If I let her eat more than that, she throws it all up. So I can't leave food out, I have to be at home all the time and just keep feeding her. I work full time and live alone, so every time I am gone for a long period of time (every day weekday) she throws up the first batch of food. I also can't leave this type of food out  because I have another cat, and if my other cat eats filets/bits, she gets diarrhea. So my only solution is to feed the cat with liver problems a spoonful of food every half hour and stay home all the time.

I took her back and the vet said that her mouth looked better, however her liver values had not fallen at all. So it wasn't a liver infection, but a "structural problem" I'm assuming this means cancer, but I don't know. I can't afford the ultrasound + euthanasia if needed and I'd rather hold out for euthanasia if needed because I don't want her to be in pain.

She is very high energy, talkative and purring all the time and begging for food constantly. Please don't yell at me for not knowing what I was getting into when I got a cat, I have had many cats pass and it was all a steady downhill where their mood went bad and I knew it was time. This cat seems very happy though, so i don't feel like it is time. My family pulled out all financial support for other stuff because they paid for some grad school classes and they don't like cats so they won't help with any care. I feel like a terrible person, like I can't take of her properly. 

The vet says all I can do is try to switch out all her foods to see if she has an allergy. I might try it, but I am afraid it will make the other cat sick. I can't really afford heavy treatment so I know if I got the ultrasound, I wouldn't be able to afford anything after that. Also, I feel very alone. Any advice or comments at all would be appreciated.

I forgot to add, she is 14 and the vet doesn't think it's a good idea to do something like surgery on her anyway. She went from 11 to 6 lbs, now she is about 7.

I am so sorry your kitty is so sick.   I know you said you can't afford a lot of diagnostics which is understandable, they can get very expensive.  What about a second opinion.  Do you have any cats only clinics or feline specialists in your area?  Not eating well and quick weight loss can be what is causing your kitty's liver values to be off.  I hadn't heard of liver issues causing the mouth issues as you describe, doesn't mean it can't happen obviously, I am not a vet.

If it is a liver issue then not eating is part of it.  What you are doing is all that can be done if it is liver cancer.

Well, my vet said we can do a liver recheck in a month which is only $100. I can do that. I've been trying to look up other stuff to do, in terms of liver treatment, online and can't really find anything else.

I'm sorry to hear about your cat. As Denise mentioned, I think you should seek out a second opinion. There's a free app called Kuddly. There are some great vets on there, and you can contact them for online consultation via email/phone/skype for a nominal fee - less than $10. It's not a solution, but you can at least seek other opinions and treatment plans.