Call your school. If the school has an honors college, they'll probably know who runs Phi Beta Kappa, and information services might, too. They should have a list.
I doubt anyone reading these essays would assume YOU'RE mentally ill just because someone in your family was. That would be like assuming the guy who wrote about raising his brother's kids was a drug addict because his brother was.
What do you think they would do if you were mentally ill, but could still do well in law school? Do you think there is a stigma still attached to diseases such as severe depression/anxiety or the like. I think I could write a great personal statement on what it is like to grow up "sick" but the last thing I need are anymore red flags, especially since the ps is suppose to be positves. But what if mental illness caused you to be a better person?