I third that. You are just fine.
You sound VERY normal to me...AnnieBrooke has a good response..
It is not necessary at 13 to be all cravy and horny. A lot of that behavior is culture-driven, with sexualized images and role models out there all the time for girls who are quite young, and you're totally within your rights to ignore them. Your hormones are probably completely normal. It's only in pornos and male-wish-fulfillment fantasies that little girls are dying to be sexual all the time. Take your time, go your own pace, and find your own path. Maybe you are bi-curious and maybe you are not, it will unfold as you continue to grow.
Your parents sound pretty closed-minded about anything having to do with S-E-X, if they are against even thinking about sex at all. The list you gave of things they disapprove of lumps a group of things together that really aren't the same -- some of them are inherent and can't be changed (like being gay), some are choices (like sex before marriage), and some are considered to be totally normal behavior, like masturbation, and for Pete's sake, everyone thinks about sex sometimes by the time they are adult. Try not to let their unusually puritanical (and confused) messages suppress you to the point where later on, when your sexuality starts to blossom, you feel wrong or bad. Whatever comes for you, it's right for you. And it doesn't need to come at 13!
Take care.