The problem is in various definitions or philosophies on what constitutes punishment and reward.
I am sure that many will say that "rewarding" someone with the same thing everyone else is rewarded with could be a "punishment" to them if they could have more (or different) without such social justice.
One of my antagonists on Facebook insists that, in the United States, "Medicare for all" is a ridiculous notion that we would all have to pay extreme amounts for, while receiving poor care. So he quickly sees it as a punishment that I see as a reward. (Well, truly- as a basic human right.) The answer would be to allow people to go beyond the "reward" given to them- allow them to buy better care than is provided for everyone. And of course, it would also be to improve the basic care given to everyone.
With justice, students get the grade they earned. It is injustice to give an "A" or an "F" to a "C" student. With social justice, we should not go so far as to reward all students with the same grade because that would punish many of them and reward some of them.
Birth defects and diseases are not rewards or punishments. They are typically misfortune. And nobody would suggest seriously that healthy people should be made to have similar defects if it cannot be removed from others. Instead, we strive to treat the handicapped with compassion and dignity. We can never level the playing field in ways that are totally "fair" to them, but we can be human. Broadly, this must apply to social justice and justice in other issues.
Whatever issue you are going to follow up with here, it would similarly have to be taken as its own issue instead of finding some broad philosophical view such as punishment and reward being a result of justice and social justice.