A few thoughts:
One, definitely join clubs - anything that interests you and that you have time for. Often clubs have administrative positions that don't involve talking to people much. In one of the clubs I was in, the Secretary just took notes, voted quietly when there was a vote, and then sent the meeting minutes around.
Two, can you think of something to do that isn't in person? Helping with a phone-calling campaign or letter-writing campaign for an animal rights or environmental cause, starting an online forum for people to talk about something, etc. etc. I have run riddle/puzzle contests via email and the internet for friends and interested parties, and I definitely put that on my application.
Three, you might have to do something about that shyness. It is a serious handicap in interviews and office hours and such, not to mention will make being a practicing vet very difficult for you. Does your school have a public speaking course? Is there a club you can join that helps people be more comfortable with being outgoing? I'm saying this because I was told by several professors, advisors, and vets that being outgoing (or being able to act outgoing) was very important for working as a vet.