Veronica is right. The more you do it, the easier it gets. I started actually teaching classes at the age of 47 - something I would never have seen coming! I would encourage you to join a group so you get involved in some activities. You can do voter registration drives, sell sodas at the school carnival, etc. Sometimes it's easier talking to people if you are acting out a role, rather than being yourself. Eventually, with some of these people, you might have some conversations of a personal nature, but, at first it is all "business."
Although I had this same type of shyness, I became a police officer. The uniform gave me instant "credibility" (it was a long time ago!) and people would listen. When I retired, and found another job that had no uniform, I was terrified! Why are people going to listen to me? And the reason they did, after a while, was because I was knowledgeable about the topic I was speaking on, and, I spoke from the heart. I knew what it was like to be unemployed and looking for work, and was able to "connect" with people.
I encourage you to learn to confront weaknesses head on. It will help you to get ahead. Inability to do public speaking holds many people back. There is an organization called Toastmasters/Toastmistresses, where people practice public speaking. I encourage you to look into it.
Finally, if your anxiety is severe, you may seek medical help. If you are one to shun pills (which I totally understand), then you may want to research holistic treatment options, such as vitamins and the meditation previously mentioned.