Yes, if you want to make a deductible IRA contribution for 2016, then you will need to amend your return.
The IRS will treat this amended return as entirely separate from your original return. If you had a balance due on the original return, they will expect a payment from you. If you had a refund, they will send you the refund.
The additional refund from your amended return will be paid by check and mailed to you.