Yes, you do.
When you amend your return, you're starting out at zero. Anything you get back on your original return you'll get back. Anything you owe with your original return you'll owe.
The amended amount (whether you are getting an additional refund OR owe additional tax) is a separate transaction.
So in your case, you'll owe on your original return, and then owe nothing on your amended, so you really don't have to even send it in..
You have till April 17 to pay the amount due with your amended return.