It's hard to say.
Do you know any more details about your ancestry? Are you able to trace it to a specific ancestor, or do you only know you have 'some Native American ancestry'?
For example, I'm 1/8th Amerind, my grandmother is of Abenaki descent. I don't "look native" though.
When I was younger I had a friend who was Iroquois, lived in Brantford and both his parents identified as 'native' and looked like one assumes Amerind people to look; despite this he was the most WASPy looking native I've ever met. Blond/red hair, blue eyes, freckles, white complexion. It's 100% certain he was partially of European heritage since eastern Amerind people are pretty likely to have some degree of European heritage, but his parents and grandparents looked much more 'Amerind' than 'white'.
The 'Crying Indian' from the anti-littering ads was a white/Sicilian guy.
http://en.wikipedia.org/wiki/Iron_Eyes_CodyConsidering it was very common for whites with some black ancestry to claim 'native ancestry' (or more commonly Cherokee in particular) instead in the US, especially in the south, if you lack specific details as to who these native ancestors were, you may wish to look into genetic testing to confirm your ancestry.
Okay, most white people in the South are not black. ancestry. Im not sure what you mean there. But I am connected to Pocohantas. My great great grandmother from Arkansas was where I trace Cherokee. I know people think its cliche to claim Cherokee- but Cherokees were the largest tribe- especially in the Southern states. Its a lot more common to be Cherokee than anything else.