What should I do about the oath I made on the Quran after my family forced me to swear falsely to deny Zina (fornication/adultery) in order to ruin things for me, and I am repentant?

If the matter has reached the level of adultery, then you have committed a grave sin, and you must repent to Allah with its conditions: ceasing the sin, feeling remorse, and resolving not to return to it, for the one who repents from sin is like one who has no sin. It is preferable to use equivocation in a false oath, but since the matter has passed, and it was to protect honor, then perhaps there is no sin in it, but you must repent and do good deeds.