Omg. I have this problem all the time, especially in my dorm -_-. One of the girls in my hallway grabbed the bull by the horns and said "Look, I'm doing Zumba, so if you hear stomping, that's what's up". But she lived in a single. I tried working out with a friend once, and everyone came in her room and watched! It was awful. They kept telling me I was doing things wrong, even though I knew I was more fit than the girl I was doing it with.
Gyms make me nervous, too. Last summer I lived with roommates as well, and what I did was go on a trail run as far away from them as I could get. I'd double check to make sure no one was around, and then I'd do my tae bo. Unfortunately, I got a little obsessive XD Now, living at home, my room is in the basement, and it's a lot easier.
Anyway, there are two things to consider: In the gym, everyone's pretty much feeling the same way you do (even those ripped guys, but they think it's all eyes on them for other reasons) but in reality, no one's actually paying attention! People really just focus on themselves. It's more likely that if someone does notice you, they might help correct your form so you don't hurt yourself, which really is not a bad thing. And being at home I just tell myself - even if I look dumb, I'm doing more than someone sitting on the couch! I won't work out at my bf's though, but we go to the Y and swim together, which was fun.
That's the other thing, if you keep it fun, truly fun, like Tae Bo for me, then you won't care because you're loving it. Classes help too. I was so nervous when I went to a Bootcamp class at my local gym, but the trainer yelled at everyone just the same (she was really mean lol) and I ended up loving it. As long as you give all you got, you're no better or worse than anyone else.