what you are saying here is very similar to protestant teachings, and it is false,
first of all, purgatory is in the bible, both old and new testament, there’s Mt 5:48, Heb 12:14, Jam 3:2, Rev 21:27, 1 Jn 5:16-17, Jam 1:14-15, 2 Sam 12:13-14, Mt 5:26, Mt 12:32, Mt 12-36, 2 Macc 12:44-46, 1 Cor 3:15, 1 Pet 3:18-20; 4:6, 2 Tim 1:16-18, 1 Cor 15:29-30.
And secondly, Jesus indeed made reparation for our sins, and took upon Himself the sins and eternal punishment for sin, but not the temporal punishment, we are able to be saved from going to hell, but that does not mean we are off the hook completely,
Jesus re-opened the gates of heaven, Reconciled us with God, and merited abundant graces for us through His passion, but we have to cooperate with those graces, and be made in like form with Christ to merit them.
and you are also mistaken about faith being apart from works, i don’t know what version of the bible you read, but here is from the official Catholic version on the chapter you mentioned -
*"Was not Abraham our father justified by works, offering up Isaac his son upon the altar? Seest thou, that faith did co-operate with his works;
and by works faith was made perfect? And the scripture was fulfilled, saying: Abraham believed God, and it was reputed to him to justice, and he was called the friend of God.
Do you see that by works a man is justified; and not by faith only? And in like manner also Rahab the harlot, was not she justified by works, receiving the messengers, and sending them out another way? "
“For even as the body without the spirit is dead; so also faith without works is dead.” *
so, we are not justified by faith alone, and faith is not apart from works.
Jesus redeemed us by His holy Passion, but we still must work for our salvation, and why? because that is the whole point of our being here, we are here to learn to love God and earn heaven, although we will never “deserve” heaven, but we can still earn it by our good works and our love for God,
God didn’t come down and become man and live and die for us just to make it easier for us, not at all, He did all of that so that we may be saved, but we still must strive for it, because that is how we learn and grow, God gives us the graces, but the effort must be on our part,
and while our sins can be blotted out, they are not instantly blotted out when we commit them, we still must seek forgiveness,
and as we are told, “Know you not that all we, who are baptized in Christ Jesus, are baptized in his death?” Romans 6:3
we are baptized in His death, meaning, it is by His death that our sins and original sins is wiped clean from our soul for the first time, but because Christ died once only, so once only can we be baptized, it is by His death that we merit baptism, so after baptism, when we sin again, what merits forgiveness then? we must be made in like form with Christ to merit forgiveness, and what merits our forgiveness after baptism is the sacrament of penance, penance is a punishment, and just as Jesus was punished in innocence for our sins, so we must undergo some suffering as punishment to merit forgiveness for our sins,
although Jesus makes this easy for us with the sacrament of penance, after all, would we not travel a thousand miles, walk across burning coals, or other manners of difficulties, to gain this priceless salvation for our immortal souls? confession is such a great gift, and a rather easy task when you think of what it could have been instead,
although confession still does not wipe the stain of sin from our souls, by confession we obtain forgiveness and receive sanctifying grace back into our soul, but we still must pay for the sin…for example, lets say a child breaks a neighbors window with a baseball, and he regrets this very much and seeks forgiveness from his neighbor, and the neighbor forgives him, and the child is happy for this…but the neighbor says, “but, the window still needs to be replaced, and so you must pay me for it”
well, it is the same with our sins, and with good reason to, because when we sin, that has a negative effect on our soul, our mind, our heart, and it weakens our will, so, to reverse the effect of sin and clean its stain from our soul, we must do penances, preform good works, pray, and do various other works of piety,
but because we may not be able to wipe clean all the stain of sin from our souls before death, so there is purgatory, because nothing unclean can enter into heaven,
and while by the blood of Christ our sins may be washed away, they are not “covered”,
God wants to make us into what we were meant to be from the beginning, He doesn’t just want to cover up our imperfections and sins, He wants us to be perfect for real!, and to do that we must do the things He has taught us, to deny ourselves, take up our cross daily, and follow Him, keep His commandments, imitate His virtues, we must put in the effort, and God will supply the graces,
well, i have to go, although i would like to say more, but i’ll be glad to help if you have anymore questions,
but my advice to you right now would be, try to get a better Catholic education, because it sounds like you’ve been taught by protestant sources, and so i would recommend these instead -
www.tanbooks.com
www.fraternitypublications.com
audiosancto.org/
alabamacatholicresources.com/index.html
catholicapologetics.info/
gaiaonline.com/guilds/viewforum.php?f=211177
drbo.org/
haydock1859.tripod.com/
goodcatholicbooks.org/
www.realcatholictv.com
alright, so i hope this helps, take care.