So, I met this girl in some 3 weeks training and we had a fling there. Now, I liked the thing b/w us but wasn't sure where do I want this to go and neither did we had the "talk" before we separated. 

Back in our towns and I invite this girl to spend new year with me and she tells me she can only come if I hope that this thing b/w us is not just about sex but can be an exclusive in future. I said I'm not sure and she asks that if I slept with someone meanwhile and I said honestly yes. To which she seems upset and decides if I really see a thing b/w us, I should visit her and that she feels bit hurt (she drank and vomited that night) that I couldn't wait to fuck someone else. Also says that we both will not see anyone else while we are dating.

I tell her, I want to give the thing between us a chance and so I visit her city on new years. New years eve she ask me to tell about that other girl and I tell her about another girl as well (I had been with two others). And she suddenly is upset that she is angry with herself for letting me visit her and that I was maybe never interested in her. We hardly talked for 2 hours and then she says if I know someone in the city so that we can part our ways. I get very emotional at this point and was crying in a restaurant for an hour. She also a bit. She says that she can see that I am not interested in her that much and she already loves me ..and this thing is gonna break her. Also, that me being with these two girls makes her insecure as she feels I am not getting all what I want from her. She also tells me that usually if her date said this thing to her,she would have asked him to leave her car.

Things get better after this. We spend the night together. While parting ways we had the "talk" again and I tell her that I am bit afraid of how fast she is going and how she talks about getting destroyed and feeling hurt. To which she again gets upset that I am trying to distance myself from her and saying such things right before I depart.

In the past she had suicidal thoughts or tried one I am not sure.

TL;DR: Am I the asshole for seeing other girls while not having the "talk" ?