If you feel like you must wear these clothes, as silly as they sound, you could try to "own it" if you will. I think all kids at some point usually are forced to do silly or uncool things as a result of their parents being overprotective or "knowing what's best."
So if someone questions why you're wearing what you are, just tell them it's because your mom's a pain. Odds are they'll be able to sympathize and have something ridiculous their parents make them do to share back. Or make fun of yourself even. "Hey guys, like my rain boots? I know it's sunny and the middle of summer, but you know, they just really make my butt look good! Which, unfortunately you can't see because of my big coat. If you did though, you'd really understand the how the whole outfit comes together. It's a work of art, really."
I know it's much easier said then done, but things aren't inherently embarrassing and if you don't want to feel that way in this outfit, then don't. Rock it! :thumbup: