What would be the purpose of that, especially if the sins of my life will hurt them? (and vice versa)
Some of the reasons we don’t know why now. But part of the purpose will be to show all (people and angelic hosts) the perfect mercy and justice of God.
CCC 1040b . . . We shall know the ultimate meaning of the whole work of creation and of the entire economy of salvation and understand the marvelous ways by which his Providence led everything towards its final end. The Last Judgment will reveal that God’s justice triumphs over all the injustices committed by his creatures and that God’s love is stronger than death.628
This will give you a little more background.
**ROMAN CATECHISM **
Reasons For General Judgment
It is necessary to show why, besides the particular judgment of each individual, a general one should also be passed upon all men.
Those who depart this life sometimes leave behind them children who imitate their conduct, dependents, followers and others who admire and advocate their example, language and actions. Now by all these circumstances the rewards or punishments of the dead must needs be increased, since the good or bad influence of example, affecting as it does the conduct of many, is to terminate only with the end of the world.
The same info. can be found in the CCC as well.
CCC 1039 In the presence of Christ, who is Truth itself, the truth of each man’s relationship with God will be laid bare.626 The Last Judgment will reveal even to its furthest consequences the good each person has done or failed to do during his earthly life:
All that the wicked do is recorded, and they do not know. When “our God comes, he does not keep silence.”. . . he will turn towards those at his left hand: . . . "I placed my poor little ones on earth for you. I as their head was seated in heaven at the right hand of my Father - but on earth my members were suffering, my members on earth were in need. If you gave anything to my members, what you gave would reach their Head. Would that you had known that my little ones were in need when I placed them on earth for you and appointed them your stewards to bring your good works into my treasury. But you have placed nothing in their hands; therefore you have found nothing in my presence."627
