Good for you for starting running also! Jogging a couple times a week will help the pounds melt off before you know it.
You shouldn't be self-conscious, although I can relate to the feeling. I liked when I belonged to the YMCA because every body shape would represent and flaunt their nakedness in the locker rooms ~ young, old, wrinkled, jiggly, didn't matter.
It felt very democratic.
Why not bring an ipod so you have something to distract your thoughts? An audiobook works especially well for this. And most of all just know that most people, no matter which gym, are thinking more of their own body than yours.
But anyway, if you can keep it up on more than just one day a week you'll see your stamina improve. I know this from the last time I was jogging regularly. You can really tell by the treadmills. You'll be able to go faster and longer, which is cool to track.
If you feel self-conscious and decide to go for it anyway, just know McDougallers like me are rooting for you and it's just a matter of time when you'll feel more self-confident because of how you'll look, time which will happen sooner the more you work at it.. at least, that's what I tell myself too..