I'm more than 10 years older than you, but my BDSM beginnings were much the same as yours, at roughly the same age, and I grew up in a conservative culture as well.
I did a lot of self-bondage and experimented in online chatrooms and roleplay MUSHes initially. The online stuff tends to get a bad rap (for reasons that I understand - personally online play holds zero appeal to me currently), but for someone who is new, young and living with family and wanting to "wet their feet" in a relatively safe and harmless manner, I think they are excellent. Especially the roleplay games, as you can pretend to be a different persona - it's like playing Final Fantasy or Dungeons & Dragons, just with a kinky twist.
Just be careful about taking anything out of the "online" world, and remember that there is NEVER an obligation to show anyone pictures, or webcam with them, or give them any real-life info about yourself.
Fast forward to the present, I am in a LTR with a sexually compatible partner who is also my Dominant in the bedroom.
The self-discovery that I started at your age was INVALUABLE in leading to this. You have the advantage in knowing what you want sexually and out of a relationship without needing to go through lots of terrible unsatisfactory Rs to get there.
More additional suggestions:
- Read blogs and articles by other female submissives. I've found submissiveguide pretty good for this, but really anything written by subs for subs will do
- Learn about your sexuality. Have you been able to bring yourself to orgasm yet? theclitoris is a good website to start with
- If you want to dabble in self-bondage, be SURE to learn the ropes re: safety and err on the side of caution. The last thing you want is to have to get your parents to rescue you....