It sounds like she isn't into you romantically, but she isn't sure how to let you down. It sounds like she is a nice person but doesn't feel the same connection with you that you feel with her, and that's okay. I firmly believe, and this is clearly a matter of opinion, that if you have to shake the head of the person you are with to make them see that what you have together is worth it, then it will never be worth it to them. If you feel like you have to convince somebody to date you, they probably aren't the right person. She should be able to say to you that she isn't interested in dating you, so that you know how she feels so you can move forward. I do think that sometimes we aren't sure if we are into someone or not, so we want to take our time to feel out the situation and see if a stronger connection grows; but I do not think it's fair for someone to string another person along if they have different expectations. I think if your gut is telling you she isn't being truthful with how she feels, then you should cut your losses and move on. There are plenty of other people out there who don't play games and who would be happy to be with you.
"Caring is not an advantage."