You'll either need to download a fillable Form 8606 from the IRS website or you can prepare one in a separate TurboTax tax file using forms mode and overrides. It cannot be prepared in your amended tax file.
Since you are now eligible for the Retirement Savings Contributions Credit, you'll need to include the Form 8880 with your amendment. TurboTax will already have included the resulting credit on Form 1040X, so your amendment needs the Form 8880 to support that change. Similarly, You'll need to include the changed Schedule A. Basically, any form that has changed needs to be included in your mailing (except Form 1040 since Form 1040X takes its place).
Your NY state tax return will need to be similarly amended. I'm not familiar with the details of amending a NY state tax return.
