Good exercise for a 13 year old?

I'm 13 years old, and I've been noticing that I don't have a very healthy diet. I don't really gain weight off of it, but I do have some baby fat on my tummy, and I'd like to get rid of that. I was thinking I'd start eating healthier, and exercising. The problem is, I don't really have any way of exercising.

-No room in the house for any exercise machine.
-I'm afraid to join any sports, because I have social anxiety and I'm very clumsy.
-I don't have gym until the second semester of gym, and even then we don't do much.
-I could go to the public gym, but it would be very embarrassing because I'd be alone and I look like I'm 11. Most people who go there are 15+.

So what should I do, and how often? Thanks. :)
Oops, sorry, I meant I don't have gym until the second semester of school. =P
 
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