Update: I like this girl however I can't ask her out because her parents are overprotective of her. What should I do?

This is basically an update of my last post

1 week after the original post, I started to notice a trend whenever I texted her. I always texted her first and whenever I didn't, she never did. It got to a point where I suspected that she wasn't into me so I decided to make my intentions clear to her. I texted her that I liked her as a person and of course, she said the same thing about me. Then, I asked her why she was doing this and if she honestly liked texting me. She responded my telling me that she's shy and afraid to text first unless she has a burst of confidence(whatever that meant). I decided to give her the benefit of the doubt and continued texting her. The next day, she texted me first thing in the morning(Wonder why?). I thought maybe she thought I was antagonizing her and that she wanted to talk to me. Turns out, she does the exact same b.s that I mentioned earlier. I took all of my friends' advice and decided to stop texting her. One of my friends gave me some good advice. "Although it is summer, you shouldn't stress myself over this girl when there are other girls you can be talking to. Hell she probably feels the same way and doesn't want to text you all summer so take it easy." So I decided to stop texting her to see if is really interested in me. So far it's been 3 weeks and I finally came to the conclusion that she isn't interested in me. I want to move on but something keeps telling me that if I stop caring about her, then went school starts, she's going to think that I stopped caring about her. I honestly don't know what to do.