Similar situation happens at my place. When my sister was my age, she wasn't allowed out, but me, being 2 years younger was allowed out all hours of the night. I think it was mainly because I'm a guy, I'm fairly well built for my age, and I can handle myself if I get in a situation. My brother is a year younger, when he goes out he needs to bring his phone and has to be with friends, someone has to drop him off and pick him up ect.
I don't exactly live in a rough area, but I've been in a few fights. I've won some, I've lost some but have never been seriously injured (just cuts and bruises).
One of my friends wanted to do a self defence course, but didn't want to go alone, so I went with her. I learnt some pretty good tricks on how to get people off you, that require little strength. They're just quick basic movements to throw your attacker off balance and onto the floor.
So maybe learning some self defence will make your mum feel a bit more confident in letting you out the house. Hell, even have some friends join you, it was pretty fun. I had a great time throwing around a girl half my size