<human>: Can you succinctly summarize the text in 1-3 sentences?

Last year, I met this lovely lady in my biology lab and we along well. We would help each other with assignments and study together. At the time, I was in a long distance relationship, so I refrained from making any additional moves. She didn't discover our age gap for a while, and always brought it up jokingly whenever we hung out.
Fast forward to this year. We've caught up and hung out several times, going to bars/pubs or chilling at each other's places. I'm single, she's single, so I asked her out. She accepted, but then called me the next day saying she feels that it was unfair to me if she went out with me as she was still recovering from a 4.5 year long distance relationship. 
That's cool, I'll be that 'nice guy' and leave it be. 
Last night, we went out for a few drinks, we had a lot of fun, she invited me to her place, but it got awkward she started wondering about her past relationship again. She offered her couch for me to sleep on, but I refused as my place is close by. We hugged at the door, and she says "maybe females and males can't just be friends can they?" I remember saying "can they?" and then kissed her on the cheek and went on my confused way back home in the cold Canadian winter.
Have I been friend zoned? Is there an issue with our ages (she's graduating and leaving next year)? Does she even like me? She talks to me on and off, depending on the exam season. I really have strong feelings for this girl, and I feel like I deserve a chance.
<bot>: I (19m) want to pursue a relationship with girl (22f), she's still getting over a 4.5 year relationship. What's the next step?