I forgot to state my estimated federal and state tax payments for 2020 in my 2020 tax return. Shall I try to amend my filing and will I be able to do it electronically?

Yes, you can e-file your 2020 amended federal tax return, but most states require amendments to be printed and filed by mail. Please see FAQ How to amend a tax return for instructions.

Please wait until your original returns have been processed to see if the IRS will make an automatic adjustment for the estimated payments.

Please, see Where do I enter my estimated tax payments? for additional information.

Did you file?  Wait and see if the IRS and state adds them on for you.  They may catch it.