Hey Ore, welcome,
I can understand your parent's decision, born in Asia as well, alot of my friend's families wanted their children to have a good career, since employment competition is so intense. And a future career in piano or anything with being a musician looked not so promising. Anyways, you have a background of music, 15 years is good for knowing structure and basic analysis of music. To become a good composer, in my opinion needs originality, unique aesthetic qualities, communication to listeners, something that makes people wanna hear it, your personal tastes, ideas and feelings in the composition, basically it should be musically rich and something you really like. Not all people can be composers though, hehe, like me, I lack creativity and structure.. since I lack attention to detail, even in playing sometimes...
Anyways, you mentioned that you wanna go into competitions, and if you win them, then you could be a composer, hehe, I think that's the other way around, you usually have to be a pretty good composer already to win composition competitions. Speak to anyone you know who are musicians, perhaps your old piano teacher, friends who play instruments, there are stuff on the net, just do a search, perhaps your area council or music community, they could offer you fun things to do such as write for a little musical or a song etc... Goodluck with it.