Should I say no I did not receive any monthly payments even though I did, but it was from the person who claimed them previously and not the IRS? Or do I say yes, I did receive the money?
You do NOT enter that the "someone else" gave you the monthly child tax credit payments. That person should have opted out instead because now your lives become more complicated. If you can claim the children on your own 2021 tax return, then you can get the full amount of the CTC---it will show up on line 28 of your Form 1040.
If you say you got the advance payments it will cause a mismatch in the system and your refund will be delayed for months.
The person who did receive those monthly payments will get a letter 6419 from the IRS and MUST enter it on their own tax return. They might have to repay that money--depending on their AGI.
If they have to repay it---after having given it to you---then you will have to be on your honor to pay them back when you get the full amount yourself.