Just because somebody is an extrovert doesn't mean that they will be successful. Regardless of your personality you need to produce good work and get recognition for it. Extroverts simply seem to be better at blowing their own horn. But if they don't produce they will be quickly found out.

In my experience you have a great deal to gain from join a local Toastmasters chapter. Not only will they help you overcome your social anxiety, but you will also gain skills to become a more effective communicator.