Can you give a cat Pepto Bismol?

You can give it to your cat, actually, but it's not going to resolve the problem as to why your cat is sick. Pink Bismuth is not actually used to treat vomiting in animals (or people, really). An elderly cat like that really does need to see a vet. Why don't you call your vet and schedule a payment plan. Almost every vet does that. Good luck.