You cannot get earned income credit if you file married filing separately but you can still get some child tax credit. Are you confusing the two credits?
Look at your 2020 Form 1040 to see the child-related credits you received
Child Tax Credit line 19
Credit for Other Dependents line 19
Earned Income Credit line 27
Additional Child Tax Credit line 28
Child and Dependent Care Credit line 31 (from line 13 of Schedule 3)
That means the $2000 child tax credit is being applied to the tax you owe. You are not getting any of the refundable part because you had a tax liability that is using all of the CTC. And since you are choosing MFS you cannot get childcare credit or earned income credit.