I feel awkward excercising or jogging?

Lacrosse season is starting sooon, so i think that i should start running. I don't have a treadmill at home, and i feel so awkward jogging outside. My town is small and i dont know where i should run, like i hate running past people i know house's because i would feel so weird if they saw me. Like i know its nothing at all to be ashamed or embarassed of, so i dont know why i think this way. Plus, what should i tell my parents? Im 15 years old, and i know they wouldnt care at all if i started jogging i just feel stupid. I tried bringing my dog with me, but that doesnt work out and is not an option anymore. Also, what should i wear? its winter becoming spring soon here and is pretty cold, so i would need long pants and a jacket. Thanks a lot!