I know exactly what you are going through because I experienced a similar thing with my parents. They had always left the door open for me to choose my own religious path but they wouldn't let me go to any church until I was 18.
I, like you, was first drawn to the Roman Catholic Church but I turned to Orthodoxy but my parents still were against any conversion until I was over 18. I didn't understand their reasons then, but I do now. There are alot of strange cults, sects and 'faiths' which set themselves up and see younger members of their congregations as very handy for the demographics of their church. When people say to them, "Your church hasn't got a huge congregation", they can say, "Yes we have. And they include this....this....this". These sorts of sects can ask you for alot including money and so, as my mother recently explained to me, she didn't want me being drawn into such an organisation at a young age when you are impressionable, even if you don't feel that you are. And remember, at the moment, there is a huge anti-Church feeling in the media which may affect your parents view of the church and they may worry about what you're getting into.
I would say that you are best off taking the advice of both of he previous posters but above all.....PRAY. Prayer will not only bring you closer to God but will fill that emptiness you feel and that you want to fill with regular worship. If you haven't already, choose a Saint and "adopt" him or her as your Saint. Pray and ask their intercession for you and I would say that instead of wondering why you are drawn to Orthodoxy, just say, "Lord, I'm yours. I'll follow you wherever you want me to go". Read the Bible and read your theology books, worship when you can and how you can. As ozgeorge said, many people throughout the ages have had to practice in secret.
I will pray you for and I hope that you will be able to follow the path you want to follow.