Advice...

So i’m 19 year old overweight girl. I want to lose weight so bad and I think I know how. I eat fairly okay (I could improve) but what i’m really lacking is the exercise. Specifically cardio, because I know that’s the number one thing that gets rid of fat. I can really push myself, I know I have what it takes but i’m so self conscious. I want to run and get really good at it but I don’t want to run in the gym because it’s embarrassing for me. Not necessarily because i’m chubby but because I have a huge (and i mean HUGE) chest and obviously they bounce and I hate it with a passion. And for the same reason, I don’t want to run in my neighborhood. The last option I could think of was a trail at a park near my house but none of my family wants to go with me and I don’t want to go alone.. (I’m a very paranoid person). I don’t know what to do... I want cardio to be my main focus but I can’t do it anywhere 😔 How else do I drop significant weight without cardio?? Or can anyone think of another solution for me to do cardio?