I originally thought I had just gotten the second stimulus payment not the first so I listed this in my taxes and filed. However, I just got a letter that was dated after I filed saying my second stimulus is coming now and I should get it soon. This must mean the payment I received was the first stimulus check. Do I need to file an amendment to correct this?
You cannot amend right now while your return is still being processed. Wait and see ---the IRS cross checks for stimulus sent to you so they will probably adjust your refund before they issue it.
No, you do not need to file an amendment. The IRS will most likely make an automatic adjustment. Please see IRS Recovery Rebate Credit Q D2 What happens if I claim the incorrect amount? for additional information.
For additional information:
If you received Notice 1444 in the mail but have not received your payment as mentioned in the notice, then you need to request a trace and claim the Recovery Rebate Credit on your 2020 tax return. Please see How do I request a payment trace to track my first or second Economic Impact Payments?