Of course it's a silly fear, but it's still stopping you, so you need to deal with it.
I had a longing to learn to belly dance, but a horrible fear of looking ridiculous, and that kept me from starting for almost 20 years. Now, I'm so mad at myself for giving in to that fear for so long!
It's a really hard thing, to get over that fear though. Eventually, I came to the realization that it really didn't matter a rat's a** if anyone looked at me or thought I looked silly, I wasn't doing this for them or their amusement, I was doing this for *ME*. And then after I started, I realized, that no one *was* thinking I looked foolish - they weren't even looking at me at all.
I'm not a big gym fan, but it has more to go with hating to go out when the weather is bad than a fear of people now. I mostly exercise at home or at my dance class, but I do go to a gym when I get bored with home and the weather is good. If you were to go to a gym and look around, you would see that most people are off in their own little worlds, listening to their music, and not paying attention to you, or anyone else, beyond an occasional glance. There are all sorts of shapes and sizes at a gym, all sorts of fitness levels and strengths. It's really hard to stand out and get everyone's attention at a gym, unless you are really trying to draw that attention. There's sort of an unwritten rule to keep to ones' self.
Naughtymonkey's earphone idea is a also good one (unless you are using a personal trainer to get started - then you do need to communicate). Another thing you can do, is ask the gym when their least crowded time is, and go then (or email them if calling makes you too anxious).
BP