Getting access to credit
Many veterinarians accept Care Credit, which is a credit card specifically for health care expenses, including a pet's. Care Credit offers multiple payment options that may help pet owners through a crisis. You can find out more information about Care Credit and fill out an application on their website.
Financial Assistance
The Humane Society has a great list of options
https://www.pawlicy.com/charity-helping-afford-vet-bills/
American Veterinary Medical Association provides a guide to financial assistance
https://www.avma.org/resources/pet-owners/yourvet/financial-assistance-veterinary-care-costs
GoFundme lists a wide variety of options, more than its name suggests
https://www.gofundme.com/c/blog/help-with-vet-bills
NYSave is another list that is specific for New York State
https://www.nysave.org/pet-owners/financial-resources/
Pawlicy has a search engine to help you find grants
https://www.pawlicy.com/charity-helping-afford-vet-bills/
MyPetChild provides a quite extensive list of potential funding
Cornell University College of Veterinary Medicine also lists options
https://www.vet.cornell.edu/hospitals/clients
https://www.bestfriends.org/resources/financial-aid-pets, there is a comprehensive list of resources that offer financial assistance for pet guardians who are struggling, as well as senior citizens, people with disabilities and people who are seriously ill.
You can also try an Internet platform such as GiveForward or GoFundMe, which let you create a personal fundraising page. They may charge a small percentage of the funds raised.
Also, contact your local animal shelter. Some shelters work with veterinarians who are willing to reduce their charges, and some may have veterinary loan or grant programs.