If you think that there is only one world then you have a problem. This issue here is that can their be injustice, can God allow injustice in the world?
If I have a pen that is mine, I can throw it in the air, I can use it or I can break or give it someone else its got nothing to do with anyone else. Its my pen and I'll do what I want it.
Likewise the whole world, what seen and unseen, belongs to God/Allah so how can you be unjust with anything he owns?
If someone believes God to be Love like the christans do then there is a problem which is better known as the problem of evil.
There is no problem in Islam we believe that both evil and good are created by God and its part of divine wisdom that someone is poor and other person is rich. I know if I was rich I would be a much worse person than I am now and I am not much good now anyway!
Muslims know that the rich of this world have more to be taken into account for than the poor. Its stated that the poor enter heaven years before the rich.
Also what the poor don't get in this world they we be recompensed any loss in Paradise.
This is with the important condition that the person is muslim because disbelieving in God/Allah means no reward.
God/Allah is alive and its part of his majestic mercy that he does not destory us for even thinking bad about him because if i owned someone and he said someone bad about me I would want that person to be punished. God/Allah, oout of his mercy allows that person to have another chance then another one to come back.
Catasphories are opportunites to go to God/Allah with an clear heart and ask.
For a Muslim problems can be one of two things
1. Removal of previous sins
Either way they are better than to get punished in this world rather than the next world.
You sound like you have been effected by Christan thought and now you need to think like a Muslim.
Think about this.