After you file

I filed in 2019 as Single, with 2 dependents. I think it should have been Head of Household. When calculating the second stimulus check, I realized as Single I get only $600, and nothing at all for the two children.

 

If I amend and file as HOH for 2019, would I be able to get the $1200 for the stimulus? Would it automatically end up on my 2020 refund? Is it a waste of time to amend?