Question

To which part of her identity is noda referring when she says that "my identity seemed to hurtle toward me and paste itself right to my face"

Answer 1

Noda is referring to her racial identity. People were racist toward her because she is a Japanese American citizen. People could tell by her face that she was not just Caucasian. Step-by-step explanation:

Answer 2

I would say she is referring to her racial identity.
She is talking about how people used to be very racist towards her because she is part Japanese (she is a Japanese-American citizen). Just by taking a glance to her face, they would assign her a certain race and treat her differently based on that.