Can someone who's an introvert become an extrovert?

You do know how it works right? The I says you have Introverted Sensing as your dominant function, you have extraverted feeling as second. Those are most present. You have introverted thinking as achilles heel type which makes you vulnerable to people who do well and abuse this, and you have extraverted intution as your inferior function.

Read more here:http://www.humanmetrics.com/personality/isfj
This site explains what it all says for example Introverted sensing:

Spoiler

As for ISTJs, the dominant Si is oriented toward the world of forms, essences, generics. Again, "for both of the IS_J types, the sense of propriety comes from the clear definition of these internal forms. ... A 'proper' chair has four legs," etc. (Jung saw IS as something of an oxymoron: sensing, which is a perceiving function, focused inward and thus away from that which is perceived (the "object"). In this light, he described this sensing as something removed from reality, full of archetypes/mythical figures/hobgoblins; sensing of one's own set of forms.)

Maybe you can figure out how you can overcome your social anxiety

 

Can a righty learn to play lefty?