I'm from the first generation in our family to be born in the US, and my parents are Indian. But I still consider myself American.
Since you're born here, you're a native American!
And an Indian.
And this is doing absolutely nothing to reduce the confusion between Indians and Indians and native Americans and native American Indians or native Americans with Indian ancestry... We all blame Columbus, who was lost as f***.
Residents of just about every state use the usual English conventions to form the demonym
Hawaii - Hawaiian, Alaska - Alaskan, Kansas - Kansan, Florida - Floridian, Wisconsin - Wisconsinite, Rhode Island - Rhode Islander, Texas - Texan, until we come to Indiana.
Things were already confusing enough, so they're officially called Hoosiers, since "Indianian" would mean "of the land of the land of the people of India".