Is this the first time you have been to therapy for any reason? Is she officially diagnosed?
I was a little nervous when I went for the first time, too. I went because I was exhausted trying to communicate, she kept insisting there was something flawed with me. I went in, sat in the chair, and told the T that I was having trouble communicating with my girlfriend. She asked me to describe what was going on. I did to the best of my recollection, and 15 minutes later the T was leaning over to her bookcase and pulling out a book called "I hate you, don't leave me".

Took T 15 minutes to suggest to me that I was doing nothing wrong, and that my girlfriend had BPD. Two weeks later, my girlfriend admitted as such - that she had been diagnosed BPD years ago.
I'd suggest just going in there and describing the problems you are having. Be honest, and try to keep it about you and about things you can do for yourself rather than just venting. The awkwardness will disappear after 15 minutes or so, and the T will guide you in the right direction.