I'm perhaps more of an extrovert in the same situation, but just apply to everything --- sure you'll fail at some stuff but it's always instructive. The key is realising the difference between a judgement of you and a judgement of how you interview :)

Hell, I got an internship last year by cold-emailing someone from the HN Who's Hiring thread and asking what they were running this year. Just put yourself out there and you'll have no problem.