Justice, in the poem "Suicide Note" by Janice Mirikitani, involves all human beings, anywhere being treated with the respect they deserve, whether one agrees with their actions, beliefs, or way of life. We mete out justice in our lives when we stand up for the dignity and the rights of others, as we can, which is not always an easy thing to do.
Justice involves not judging others, because we do not know the inner turmoil others face in their lives. We are not to judge people - we may judge actions - in the sense that we know, based on the moral principles of society and religion what is right and what is wrong. We do have an innate sense of right and wrong. Consequently, we make judgements in society, for example in our courts, as to what is right and lawful, and what is wrong and unlawful.
In this poem, justice would involve the parents treating their daughter with fairness, on an equal footing as if she was a boy - which this girl feels her parents wanted all along. Justice, to this girl who committed suicide, would be extending comfort, help, and support to her as she struggles to make good grades and struggles to make her way in life according to her dreams and goals.
"Just Us" in this poem alludes to the fact that it seems, from what the girl writes, that her parents are looking out for themselves and their desires; they are looking out for "just us' and not listening to and promoting the dreams and wishes of their daughter. They most definitely mean well, and want the best for their daughter - but on their terms, not the daughters - this is the "injustice" in the poem, and in the girls' life, and the "just us" attitude of the parents.
This is something that the parents may not even have realized that they did. However, the daughter sees herself as a disappointment to her parents and she cannot face letting them down anymore - nor can she face her life struggles anymore.