Take a look at your insurance policy before you do anything about your claims. Read the policy, review your deductibles, determine the procedure, but act quickly so that the insurance company can't disclaim coverage for untimely notice. Yet, read your policy and learn your rights. Remember, insurance companies are not excited to pay claims and you need to be a great advocate for your own rights, you may even want to hire a lawyer if you get into a dispute with your insurance company about coverage. If you believe that they should pay based upon what your policy says, don't just take their denial as being correct, fight it. Be clear, each policy is different, so you have to read your policy before you act.
It's likely you have a Hurricane Deductible in your policy. New York is one of many States that have Hurricane Deductibles in homeowners' policies. These deductibles are a charge of a percentage of the claim, instead of a flat fee, prior to the policy paying. Some are in the neighborhood of 4% of a claim. So, it can get quite pricey. The States (territories) that have these deductibles are Washington DC, Alabama, Connecticut, Delaware, Florida, Georgia, Hawaii, Louisiana, Maine, Maryland, Massachusetts, Mississippi, New Jersey, New York, North Carolina, Rhode Island, South Carolina, Texas, and Virginia.
The reason it's a good idea to look at your policy is that this deductible may not be triggered by a tropical storm. Each policy is different, but the downgrade in the storm may have saved you thousands of dollars in your deductible. Good luck.