I'm a bit older than you but I was in a similar boat once. I was into this, my wife wasn't. I'd sneak reading or studying and feel really bad about it. I went out of my way to read all of the anti-LDS material out there in an attempt to make the draw and obsession go away. For a long time I struggled and was super depressed, then I just kind of got over it and told my wife I was going to read and do me but I wouldn't push her and she could do whatever she wanted. It didn't work out in the end, I don't know quite what I believe and I don't think nearly as much about it now as I did a year, month, or even a week ago. But I feel sorted and I'm glad that I got to think about it openly while being honest.

Your parents are your parents. They're going to want you to think and believe as they do, not to control you, but because the obviously think that what they believe is correct. And when you love someone, you want them to live correctly too. How do you move forward? I don't know your parents so that'd hard to say but, I'd encourage you to be honest. Don't try to convince or convert them of anything. Just say that you like it, believe it, don't want to be mocked for it and would be completely into not talking about it at all. If that doesn't work you're just going to have to wait it out.