Junior has to conceal his poverty because he recognizes that he is being targeted at Reardan for so many elements. Poverty would be used as another reason to target and marginalize him. Junior understands that this is the condition in which he lives by being one of the only Native Americans at Reardan. Junior clearly recognizes that he does not have much in way of resources or defense at Reardan. He keeps his financial condition to himself because he understands that he does not want to be further targeted.
Another reason that Junior keeps his financial condition a secret is because Reardan embodies a collection of wealth. When his father drops him off on the first day and tells him that "those white people aren't better than (him)," it is a statement that is as much economic as anything else. Junior understands that he enters a world of wealth and privilege. There is nothing to be gained in disclosing that he does not share such a reality. Penelope offers to collect money for Halloween and give it to those less fortunate. Undoubtedly, one of those people would be Junior and his family. Nothing is gained socially or emotionally from Junior disclosing his financial challenges to a world that does not experience much in way of financial challenges. This becomes another reason why Junior keeps his financial condition private.