I'm pretty shy too, and the way I get over this in situations where I really can't be shy is:
Act.
In an interview? With a person who's never met you before? Well, they don't know you're shy, so pretend you're not.
Imagine you're in the shoes of a confident person with a voice that can be heard. Perhaps think of a character from a show or something who's got a calm but self-assured vibe, and act as if you're them.
Rehearse your 'lines' beforehand (which you should be doing for an interview ANYWAY), and once you know what you're talking about, even if the conversation takes an unexpected path you'll be able to improvise.
It may seem like it's not being 'true to yourself' but if there's a part of you that you have to change, that's a sacrifice you have to make. Once you act confident enough and enough people start seeing you as confident, you'll start to realise that you're not as socially rubbish as you thought and that confidence in yourself will become real.
I've recently been recommended the Alexander Technique to improve my body language and help me come across as less awkward or tense in social situations. I've not tried it yet but have a look if you're interested. http://www.alexandertechnique.com/