I had a similar problem when I was younger. I shared a room with my sister. I discovered the wonders of "taking a bath." You can go into the bathroom and no one will question that you're spending a long time with the door locked or that you don't want to be disturbed. It even helps to explain away things like burning candles or incense.
It's only a temporary solution though. In the long run it's much better to talk to your family so you don't have to be so secretive.