Some food for thought:
Who would you consider the ultimate alpha-male? I mean, the greatest alpha-male who ever lived?
Think about Jesus Christ for a moment. Whether he really is God the Son or not, I'm not going to preach upon you guys, although I believe he is, but even if you are not Christian, you have to give Him credit for being the ultimate alpha-male. He was very, very confident. He would say to someone "Follow me." and that person would get up from whatever they were doing, follow him, and leave their past life behind. He was not afraid of pissing people off either. What He was teaching pissed off the pharisees, sadducees, teachers of the law, the Romans, and the Jews, and more groups that I am probably forgetting. He was tortured and crucified for what is right, for His mission in life, for His beliefs. He is caring and compassionate, but is definitely not a "nice guy". He talked, and people listened, and today He is the most worshipped God/man in the world, and the book based off of His life and death is the best selling book ever.
That is alpha for ya. Think of others who were not bothered by what people thought of them. - Theodore Roosevelt. Franklin Roosevelt. Rickey Henderson. Babe Ruth. Even George W. Bush. Like him or not, he is an alpha male who takes no crap from anyone, and does not let himself and his country get walked on.
Now think of who got where they were by worrying what other people thought of them - ... Can you think of anyone? Me neither.
Point is, those who care are followers. Those who do not are leaders. I know this isn't exactly real advice, but if it inspires you and makes you think a bit, then just as well. As for what to do, try new stuff. Learn how to have fun by yourself, and to strike up conversations with complete strangers. It's great fun, and improves confidence.