Can NY State levy my bank account - for back taxes owed - if the only income I have is from Social Security?

Yes, they can. They cannot touch your Social Security, but other funds in the bank account CAN be levied by the state to pay unpaid taxes.

The issue will be now, you will have to go to the court and prove which of the funds is your social security and which is not. They can keep funds frozen

Once funds are deposited in a bank account there is no indication of where those funds originated from.

If you know you are subject to a judgement or tax levy, then you need to inform your bank that the only funds being deposited are from protected sources. If the account has already been levied, then you need to go to court and prove that the only source of funds in the account are from protected sources.