Hi,
I think I will say 2 things.
First,
I don't really think you would have a problem with justice.
I mean if some person murdered your family in some horrid way in cold blood you wouldn't mind him being judged for it.
So, the problem might be in that you do not think God is being just in sending men to hell.
This might root from you not thinking mans sin is bad enough to deserve such a punishment.
The fact is though that sin is a very weighty thing.
Especially when seen in the true light of the true holiness of God.
Man is not only accountable for lying or sinning against man but against God.
The Gospel which is a lofty mercy from God raise the bar for accountability. A great salvation if neglect leads to a great judgment.
When one sins against an eternal God they receive an eternal judgment.
Not only this, but when one walks proudly before God if His anger is justly kindled he will take more then an eye for an eye. For instance if a man took the life of your child his life would not be enough to satisfy your desire for justice. You would be so righteously angry you would want 3 of His.
When a man sins against God they are not just sinning against anyone. They are sinning against a King, a Savior, the Groom of the Bride the Church, against "God" who receives all glory and honor, ect.
We do not see the weight of sin until we experience it. When we sin against someone it is not so bad. When they sin against us it is huge and that person so evil for we feel the consequence of their sin.
We have a problem loving our neighbor. We are offended to the person next to us because we are effected by them relationally, but not so much the man across the world. However, God is relationally connected to every person in the world even more so then we our neighbor for even their hearts effect Him. Imagine billions of people with bilions and billions of sins all touching the heart of God personally and imagine if you had to endure that when you cannot even endure a couple from your neighbor.
In addition look at what the world has done. World war 2, slavery, human trafficking, neglecting the poor, pride, fellowship with darkness, and a hate for God by loving sin.
Secondly,
It is not as if everyone gets the same amount of judgment. I know that all who are not with Christ will go to the lake of fire for eternity, but there will be different levels of punishment therein. So Stalin, Hitler, and others will be judged much worse then others.
I will end by saying that I empathize with you in some sense. I mean some are offended by earthly judgments, but neglect to think of those coming later. This is largely due in part to not believing it or not being sincere enough to acknowledge it. So, I respect the fact that you are looking at things truthfully. This though is in fact the truth. This truth is not easy to receive. If it were easy to receive it probably would not be the truth. This great judgment speaks to us of the great sacrifice and love God has given us in Christ. It speaks of the great evil of mankind to deserve such a penalty. It speaks of the greatness of God and His lofty holiness and love and eternality.
In the end you need God's help to receive His word. I know even after being saved that I have had problems with doctrines like these. I wrestled with them fervently in my head for seasons. I thought and thought and though that helped some I in the end had to lean into God for grace. God has shown me grace and taught me things though hard are true and right and love uncompromised in the beauty of His holiness.