Is it still worth pursuing?

In May I fell in love with a girl. A few months went by and it wasn't until September that I got the courage to talk to her. I am 17, and this was my very first attempt to start a relationship. We became great friends and I realized that she was very interested in me, we even flirted, and then... I confessed that I liked her. Surprisingly, she said she felt the same way, and told me she would date me. We continued to have fun together, but then I started to act needy and clingy. I wanted her attention every day, do what she was doing, and I also didn't gave her space until she... broke up with me. I think I bored her.

After the breakup, I apologized and went after her and gave a chocolate. That didn't work. Then, almost two weeks after our last contact, I broke the no contact rule and texted her on a social network, and again, she pushed me away.

Is there still a chance she will come back to me? I really kept pushing and apologizing after the breakup. Or should I move on? She is really special to me... first love, dammit.
Is it still worth pursuing?
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