>>1 the part of you that doesn't like her is your mind's rational, the part that likes her is well your "heart". Love can be irrational and the part of you that's saying no is just afraid of wasted effort. This seems like a romance novel X3
Try thinking from her perspective, she might not be ready. You're both young and in highschool and she could just be avoiding a relationship so she can better focus on her studies. She might be too shy to confront you in person.
I think you should wait for her, but don't wait forever, a couple more years if necessary. You talked well online, try doing that again. She might be more comfortable online.
The thing is, you need to decided for yourself whether or not she's worth waiting for. From what you've wrote, it seems like you really love her and I think you should wait for her. I'm also waiting for someone special and what I did was tell him that I'm giving him around two years and then I'm moving on. Perhaps tell her that you're waiting for her to be ready to have a relationship but give her a deadline per say, she needs to know that you won't wait forever.
I wish you two well~! I hope that helps :3