I started running when I was 14 and know where you're coming from. At the time I hated them being overprotective, but now that I'm older I understand why. I'm not so worried about a random stranger attacking me. Sure, that happens on rare occasion, but there are plenty of other reasons not to run alone. For example, you could get fall and injure yourself, get lost, etc. These are my suggestions:
1) Find a running group. Most towns have them. You could also contact the coach at the high school to see if you can train with them. My high school team let junior high kids practice with us.
2) Run at a track and/or around athletic (football, soccer) fields. I did this a lot during winter when I started running because my parents didn't want me running alone in the dark. My dad came with me to the track and walked laps while I ran.
3) Have a parent follow you on a bike or in the car. Mine did this a lot on my long runs because I always insisted on running them out in the country.
4) Run inside your school (after hours). We used to do this when the weather was bad. Super boring, but better than nothing. We also had a big basketball arena with some serious bleachers. I'd run those for "hills."
5) Run around your block or up and down the street. That would get old, but way better than running inside your house. How would you even have room for that? Even prisoners have a little bit of outside space to work out.
6) Join a team at your school. Do you have a track team? Soccer team? At your age, you don't need to do a lot of miles right now. The high school coach won't and shouldn't expect you to be running as much as the older girls. You can be in plenty good shape from playing other sports.
7) If you still want to build endurance, I highly recommend swimming. It will improve your cardiovascular system without taxing your body too much. Trust me, you do not want to overdo the running at age 13 if you plan to run and improve as you get older.