The evidence that best supports the inference that the teenaged Alvarez just wants to fit into American culture is found in the following line:
"They were just being curious, I knew, but I burned with shame whenever they singled me out as a 'foreigner,' a rare, exotic friend."
This line indicates that Alvarez feels uncomfortable with her identity being highlighted as different or exotic, which suggests a desire to blend in with her classmates and be accepted as part of the American culture rather than being viewed as an outsider.