You are confusing two credits. The child care credit is the one for paying a babysitter or daycare facility to take care of your child so you can work. Only the custodial parent can use that credit.
The monthly advance payments that were sent between July and December were for the child tax credit. If you received those payments you should have letter 6419 from the IRS. If the payments were not sent to you--under your Social Security number then you say you did not receive the payments.
If your ex received them and is not claiming the child for 2021 then she might have to repay for the advance payments--that will depend on her 2021 income.
If you are claiming the child for 2021 and did not receive the payments last year then you can get the full amount -- $3000 -- on your 2021 tax return. It will show up on line 28 of your Form 1040.
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