She asked me for a second chance? Do I give it to her?

Three weeks ago I broke up with my girlfriend of 11 months. We both love each other very very much. She's headed to grad school in Maryland and I am staying in New York. I saw her yesterday to wish her well and say goodbye we met for a few hours. Nothing felt very different when I was with her. I broke up with her three weeks ago because I was tired of petty arguing and explaining myself and having to prove myself to her. She wasn't hearing me. She told me that these last three weeks of been pretty shitty and she has learned from her mistakes and she knows that if she had the chance she would make me the happiest guy ever. If I were to give her another shot it would be long-distance automatically. We would be four hours apart. Some of my friends think now is a good time to split an experiment with other people and see if we find our way back to each other. I do miss her but I'm literally split 50-50. I don't know if she's the one in the only way I'm going to know is if I get to know other people. But how loving and kind be if I won't even give her a second chance? It's not like she cheated or anything. Let me know what you think