I would rather try to find a solution to get more hours behind a PC. If your parents do not allow it then explain what you are doing instead of playing games and involve them in your project. This can give good motivation and feedback for you as well. But I don't know the exact reason why you can only spent a view hours each day. If you don't own your own PC then build one yourself, if you are lucky you can get a pretty good one for just $25. Plenty of people that can help you with it on hardware forums.
Making notes and looking up sources is a good idea for your spare time but you cannot try it out and for a lot of things you need to go back and forth between documentation and coding.
Anyway, 3 hours multiplied by 30 days is still 90 hours. Creating a full (yet simple) game in 90 hours is totally doable if you have some experience. So finishing up half a game should be possible, depending on the game of course. For a competition this long most people can only commit about 3 h/day = 21 h/week since they probably have a full time job.