Pets for Life NYC (PFLNYC), a program of the Humane Society of the United States, helps people resolve problems so they don't have to surrender their pets to the City's shelter. PFLNYC offers free and low-cost behavior training, reduced cost veterinary services for those who qualify, free or low-cost spay/neuter resources, foster homes and reduced-cost boarding for pets of people in crisis, landlord-tenant pet related assistance, allergy and shedding solutions, and general guidance and support for pet guardians. You can find information on the web at https://humanepro.org/pets-for-life/about or use this contact information:
Joyce Friedman, Project Director
Jenny Olsen, Project Director
At http://www.animalalliancenyc.org/media/ootc/2011-04/help.htm, there's more information about PFLNYC, and there's also information about 5 or 6 other organizations that may be of help to you. At the bottom of the page it says, "The one thing pet owners should know is that no matter what problems they're having caring for their pets, they are not alone!" Let's hope they've made it fairly easy to find the resources you need.