honestly i was the same but just stop caring!! these people will not even think about you in a weeks time so what's the point of feeling weird about it? I used to go the gym a year ago and i can't remember a single person there (i went for 6 months) except from my friends.
just plug your music in, maybe bring a friend and do it together. also a lot of people at the gym feel the same way, even the attractive people. they go to the gym because they're worried about their self-image and their health so just don't feel weird about it. we're all in the same boat! just be yourself and use the money you spent on your membership well, else you'll regret it