Have you applied for Care Credit or asked the the emergency vet for a payment plan? I'm sorry.
There is no answer anybody on YT could or should give. Your pup needs to see a vet right now. Most vets aren't going to even offer an option of signing your pup over because even if they now own the animal, where would they get the money to treat it and who would they rehome it to... Vet hospitals aren't rescues, so that's not something that's done often. The other option is a rescue. It sounds like there are still options available though. I'd get on the CareCredit site right now and try to get an approval. If not, I'd call every ER vet within about 3 hours to see if anybody will take payments. If your regular vet has an ER number, that would probably be best.