I'm what you would describe as a light skinned Puerto Rican woman, and I would never use that word nor any other slur.

I do want to comment on that colorism is a big issue in Puero Rico where being fair skinned is more praised. Almost all Puerto Ricans have African ancestors, to be frank these were people forced from Africa to PR as slaves, but for some it can be the majority of their ethnic background while for others, like me, it's only ~14%. The first group would most likely identify as Black, African American, and/or Afro-Latino while the second would most likely identify as white, European, or Hispanic.

If this kid is dealing with racist/colorist family praising his presumes lighter skin tone while mocking his presumed darker siblings, why we would idenify as Black makes much more sense. He is, in his confused teenage way, supporting his siblings' ethnic identity and his own as Puerto Rican person with African ancestry.