Remember other people feel the same way even if it doesn't look like it. Lots and lots of people feel shy.
Apparently Mark Twain said,
"Dance like nobody's watching; love like you've never been hurt. Sing like nobody's listening; live like it's heaven on earth."
which is dead easy when you're on your own, but not so easy when other's are around!
I really know that sense of awkwardness and fear of making a fool of yourself, plus the thing about not knowing what to say.....
ummm... but so what? People do silly things, put their foot in it, not know the right thing to say. It doesn't matter - you're not doing it on purpose and people understand that. Much, much worse are the people who are mean and calculating, who couldn't give a damn about how others feel.
Just be yourself. Next time you really want to say something take the plunge and remember the world won't end if it doesn't come out quite how you wished it would. My mum always said people are far too busy worrying about how they appear to be worried about how you appear - and she had a good point!
Keep practicing a little bit at a time - there's no rush. I promise you it gets easier over time. At one time I was too scared to open my mouth in public, nowadays I teach - which means I have to open my mouth in public! (That didn't happen overnight of course.) Good luck and keep chipping away at it. After all, you have as much right as anyone else to be ok with who you are.