I am quite shy in unfamiliar situations - and like you, don't usually say anything if I don't feel there's anything to be said. But I'm actually fine with patients - you're there with a purpose, not just to make chit-chat, and I find that sort of thing a lot easier to handle.
The prospect of having to talk to a lot of strangers (staff and patients!) some of whom may not be very nice, or not know what you're talking about, seems quite daunting, but you'll get used to it. You don't have to be massively outgoing; in fact in some cases a quieter, slightly more withdrawn manner can work in your favour.