It’s worth remembering that not all colleges want or need loud, outgoing, extroverted kids. They don’t have a list of who they want to admit based on introversion and extroversion.
They do want kids who will be involved in campus life in some way. My eldest (didn’t attend Rice) fit the description of a quiet introvert. She learned to navigate the crazy activities and went to at least a couple of parties in her time at college, and she may have had a beer or two 
. Her college involvement centered primarily on being involved with the tutoring center, TA’ing and peer advising for FYS. Colleges need those kids too. There will be a place for your child at Rice.