Morality isn't for a single person. It also concerns everybody and may be the foundation of laws.
The difference with justice is that it is applied at an individual level, whereas justice is applied by a function ( the judge as a judge, not the judge as a person ) which stands for all the society. This is why, sometimes, there may be an opposition between personal morality and what is edicted by society. All this is a problem of ethics, i.e. of application in the reality.
By the way, if morality only depended ( or depends ) on individual, it would be far more ponderous, for you would be responsible for all you do in front of everybody. An individual absolutely free of morality is an illusion. Sartre showed it quite well in
Existentialism is a humanism.
