Is anyone here indigenous American?

Hi, so I have never known much about my mother’s side of the family. On my father’s side he is white and was born and raised in Germany. On my mother’s side, all she really knew is that they were from Tennessee for generations but was never close with her extended family. Recently I took a DNA heritage test and it showed that the majority of my DNA (over 60%) is indigenous American and the other was my dad’s DNA which was German and Western European. So this really intrigued me. I tracked down my mother’s sister who she has never known (different moms, same dad). We exchanged some messages and she gave me the contact info for my paternal grandfather’s sister who is still alive (I never knew my paternal grandfather who died way before I was ever born). His sister explained to me that my great grandfather was Cherokee and everything beyond him is Cherokee/Shawnee Nation. This was really blowing my mind because my mom didn’t know anything about it and she’s really pale lol. I however have long dark hair and olive skin. My dad always said that was the European in me. I guess not. So my question is, should I go forward with this? Should I contact the Cherokee Nation and see if I have familial records through them? Would I be eligible for citizenship? I hope these are not offensive questions. My whole world just changed because I never knew this part of my story. Thank you for your help.