I still don't like phones very much. I hate having to answer them at work because I'm always afraid it'll be someone wanting something I can't do for them, or ringing to complain, and I've never been told what to say/do about any of these things (the joys of temping!)
However, when it comes to ringing other people, I actually find it much easier ringing someone with a specific purpose (i.e. a bank or, in the OP's case, a university admissions office) than ringing someone just for a chat. This is because I have a set objective, I have something to achieve by the conversation so I can go about getting it, rather than it just being for a non-specific discussion.
You might find it easier if you either write down or at least formulate in your head some kind of structure to what you want to say. Keep the first bit short, in case you need to be put through to someone else (you don't want to be giving your life story lots of times!) - e.g. "Hello, I'd like to ask some questions about admissions for X subject." Once you're speaking to the right person, have a list of questions (mental or written down) and just work through them. I find if I have a mental plan for the conversation it's much easier and less scary than if I'm just ringing someone without quite knowing what to say.