Yes, you can file your 2017 New York tax return in. You will need to mail it in. As your New York return is based off of your federal tax return, you do need to file both.
As for your 2017 federal taxes, you could potentially face additional penalties and interest if you do not file it as soon as you are able to.
You can file it and submit an installment payment plan request if you need with the IRS. See the following link for instructions on how to do that. This will allow you to set up a payment plan with the IRS to pay off your debt.
IRS payment plan options
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