I don't think that there can be one answer to this. The personal experience of internalized oppression that a particular group feels is one that spans the experience continuum. I would suggest that one answer is not going to be all encompassing.
Yet, I do believe that one personal issue of internalized oppression that many children of color have to overcome, especially African- American children, is the stigma of "Acting White." This is a condition in which certain habits are associated with a particular racial group. The label is used in the worst of senses to ensure that specific children "act" in a specific way. I think that this could be a personalized and oppressive hell for many African- American children. Consider what the President himself has said on this point in 2004:
Go into any inner-city neighborhood, and folks will tell you that government alone can’t teach kids to learn.They know that parents have to parent, that children can’t achieve unless we raise their expectations and turn off the television sets and eradicate the slander that says a black youth with a book is acting white.
The idea of a child of color with a book is "acting white" is a condition that reflects the personal experience of internalized oppression. To have to endure the criticism of doing something different and then having to be marginalized for that difference in being representative of another group can constitute as internalized oppression. At the same time, it is an experience that White students do not have to endure. This experience of internalized oppression is a social construct and a personal issue for African- American children. I would think that this could constitute as a personal issue of internalized oppression that children of color, especially African- American children, have to face and endure.