This is it guys, Today is Day 1. Help overcoming a fear of exercising in public?

Hey guys, finally deciding I'm going to dedicate myself to weight loss, I'm doing a ketogenic diet because I'm an extremely picky eater and don't think I can overcome it. The fats and proteins are what I eat normally but with a ridiculous amount of carbohydrates from snaking on junk food. I'm not getting proper nutrition though because I'm just really bad about eating veggies. It's something I want to eventually overcome but its just too much for me right now, I'm taking multi vitamins in the mean time. I know its not perfect for other health reasons, but never the less its definitely a big step up from what I was doing to myself.

My biggest hangup is exercising in public. This includes gyms but also something as simple as going for a run around the neighborhood. I know its silly and its just in my head that people are judging (or if they are, fuck em'.) but it's still hard to get out of my head in that regard. That being said, its 1:20 AM and I'm going for a run, it's gotta happen. Any tips for the day to day?