Reading the genealogy of Noah's family the prophetic curse over Canaan is evident. Gen 10:15-19 shows their family heritage. It was full of rebellion, sin, and opposing the Lord. Read and study the genealogy.
"Curse" is mentioned 89x in the Old Testament and only 12 in the New Testament and curse has a different context in the NT.
Gal 3:10-13 tells us why, "For as many as are of the works of the law are under the curse; for it is written, "Cursed is everyone who does not continue in all things which are written in the book of the law, to do them." But that no one is justified by the law in the sight of God is evident, for "the just shall live by faith." Yet the law is not of faith, but "the man who does them shall live by them." Christ has redeemed us from the curse of the law, having become a curse for us (for it is written, "Cursed is everyone who hangs on a tree")"
You're not cursed. Your family's not cursed. Redemption and restoration are in the finished work of Jesus. There's no curse in Christ and you're in Christ. Christ breaks the curse of any family history when our faith is in Him. Trust that and pray for those still under the curse of sin and shame.
-To Know Jesus. To Live on Mission.