If I gift money I received AFTER filling for FAFSA, do I have to report it to my school or FAFSA?

You don’t have to include it on this year’s form because you didn’t have it yet. You will have to report it next year. Why not use some of it for college so it benefits you instead of giving it away? Student assets are assessed at 20%, so for every $1,000 you have (above ~$6k, I think) $200 will be added to your EFC. If you have money to help fund your own education, you’re in a better position than most students

If you intend to get it back from these family members it’s not giving it away, it’s hiding it. You still have to report it. If it’s a lot of money, there are ways to minimize how much will be added to your EFC.