I know exactly how frustrating that can be. I have the same difficulty. When i was in therapy, i used to plan what i wanted to say all week before the session and repeat it over and ove in my head, but when i actually got there all that would come out would be jibberish, if anything at all.
I was actually talking to a friend about it recently, and I'll share the advice she gave me. I've only just started doing it myself, and so far so good.
The thing that i find that makes it harder to open up is a fear of being judged, laughed at, or some preconceived reaction. Try starting by giving people genuine compliments, tell them how helpful they are, the way their hair is styled looks good, things like that. Apparently, after a while, the apprehension lessens with these people and you feel more comfortable with verbalising the more difficult things. (I hope i explained that ok)
As I said, I have only just started with the whole complimenting thing, but the friend who suggested it said she used to feel the same way, and it did wonders for her.
Just a suggestion.