I listed my estimated tax payment as an expense and a deduction. Should I only list this as a deduction?

It is neither an expense or a deduction. It is a payment, under the IRS pay-as-you-go system, just like the withholding on your W-2 would be.

The payment is, however, entered in the Deductions and Credits portion of the program. See the screenshot below.

I entered it under deductions and credit. However, there was also a section in self-employed income and expenses that had a section on taxes. I listed it in that section too. Should I remove it from that section?

Yes. Was my original answer not helpful?

Ok, thanks. I just didn't understand why the business section asked about this payment, If I am not suppose to list it there. However, I will follow your direction.