If you are very introverted, then some of the companies that do collaborative whiteboard interviews would probably be a poor fit for you. The reason they interview that way is because they are collaborative work environments, or at least they like to see themselves that way. Extreme introverts, even highly skilled ones, might not fit in.

However, if you're experienced and skilled there will always be work available. You'll probably do OK. Overcoming your social anxiety would probably open some doors, though, and not just in management positions.