Thanks for starting this thread KiaKaha and getting people to think about this. It's definitely a neat philosophical question that I've thought about before. Some of my problems with social anxiety has been I've always felt I was different because I liked to think and talk about life like this and not just about celebrities and going to bars and getting drunk.
You could be a nice person all you want though - the thing is with people is that they tend to all stick together kind of like a collective mob mentality. What *if* no one does realizes that you are 'nice' - because of an attached stigma or prejudice toward you? You could be nice till the cows come home, but if someone has made their mind up about you then being nice is completely negated, even if you really are.
Just my opinion, but to stick with what I've said then you'd still be nice

Even if every other person in the world thinks you are mean, if you really are nice and you believe you are nice, then its my belief that you are nice. So I'm kind of challenging your idea that you are what other people think of you, which believe me I really understand and it makes sense. To repeat, I believe that you are ultimately only what you think you are and believe you will be, because only you can change your life.
But this is where your belief in yourself and your own thinking comes into play, and not letting what other people think of you limit your life or change your own thinking and beliefs. Imagine how many black people challenged what white people thought about them and said about them in order to get equal rights and believe that they should no longer be treated as slaves.
You spoke of people in power. We can look at this from a micro or macro perspective. People in power can be prejudiced and they may see things that are biased that could affect entire groups of people. Just look at the whole gay marriage thing. You have politicians in power who think that it's wrong - and will bestow their personal belief onto an entire populace. So in that respect (and again just one of many examples) you cant do what you want to do.
On the macro level I agree with what you are saying that prejudice is a horrible thing and people or groups in power have brought down many other groups of people. And yes, I agree with what you are saying that the way other people perceive you determines how they will treat you. The best thing about this in my opinion is that this is changing drastically in the last 100 or so years to different types of groups including blacks, gays, and women. But yes it still affects many people negatively of course, including quiet people, introverts, and people with social anxiety.
On the micro level I think there is the philosophical question of how people think of us and then I think there is the question of what are we going to do about it or how we let that affect us. The second part of that is what I'm focusing on I guess. I think that in order to improve your life that you need to change your thinking and believe what you want to be and forget about negative thoughts or perceptions from other people. I think that what you believe of your current self and future self is most important and that you should not let negative perceptions from other people affect your own thinking. Utimately they cannot change you into what they think you are; only you can change your thinking and be what you want to be. So in that sense, you are ultimately only what you think, not what they think.
A book I think you would like is 7 Habits of Highly Effective People. It not only talks about specific things to do in your life to guide you to achieve what you want, but it actually starts the book with exactly what you are talking about. About people's perceptions being different and about our perception of ourselves, other people, and everything else in life. Another great book, that talks about believing in yourself and the power of your thinking is Think and Grow Rich, which is really about achieving any goals, not about getting rich. Those are good books to read when you want to not just think about the philosophical questions you are asking, but decide what you will do with your knowledge about people's perceptions and your own thinking. And how you can use that to accept the way the world is and improve your life through your own thinking and actions.
The most important thing I think is that you are asking these questions. Keep asking them, but also think about why you are asking them. Are you asking them so you can be mad at the world for wrongs that happen to you and others. Or at some point are you asking them so you can find out what you should do about that and how you can best accept the world as it is and use that knowledge to improve your life. A bit of both is good, but I would encourage anyone to think about the second part of that if they want to be happy or successful in life.