I use the term "Native American" for clarity, since Indians are people who immigrated from India or their descendents. The term "Indian" is completely incorrect when applied to the indigenous people of the Americas, the vast majority of whom have no Indian ancestry and have never even visited India. I was acutely aware of this fact when I was vacationing overseas and explaining dreamcatchers to an Indian.
The bottom line is that we need a better generic term to describe the indigenous people of the Americas. I am also a native; almost all of my ancestors immigrated in the 1600s. The "Native American" ones immigrated earlier.
How about American Indigene? it even sounds similar.