On 2020 tax return, I included my 1st Econ Impact Pymt (EIP) but NOT my 2nd EIP. My actual refund is less than the one I filed. Should I file an amended return now?

I filed electronically Feb 12th and the IRS accepted it that day. Afterwards I realized that I mistakenly hadn't included the 2nd EIP which would have reduced my refund.  I have not yet received my refund or been contacted by the IRS.
1: Should I file an amended return now or wait for the IRS to contact me?
2: Since my 2020 AGI is lower that my 2019 AGI, will the IRS use my 2020 AGI for calculating the 3rd stimulus even though my 2020 return is in limbo?