Hi mrh125,
Only you can answer that question, do you feel a genuine connection to your heritage? Can you demonstrate that you have a true interest in your cultural identity? If so, 10% is merely a number, and it would be very rude for any adcom to even ask the question of blood quantum in my opinion. I am Native and am tied to my community strongly, and you will never, ever here that question asked of another person who self-identifies as Native. If you truly believe this is who you are, never let anyone tell you otherwise. Federal recognition has no connection to your status as a Native in the eyes of other Natives. Medical schools are going to be very interested in how this identity has influenced the physician you want to become and it will be discussed in the interview. If you are box-checking it will likely be very apparent. Don't let any non-native judge you on the 10% number.