So confused on what to do, 5 months talking to her....

So ive been talking to this girl for about 5 months. We're both 20 and go to the same college. We both really like each other a lot. Despite this, I am very unsure about if she is being serious with me or not. I have two scenarios/questions that are related to each other and need an outsiders perspective on this situation since all my good friends claimed that she does not deserve a second chance and I should break things off with her.

1. Since the time we met we've been hanging out frequently (several times a week) and texting almost everyday for long periods of time. When we hang out we always talk/cuddle and kiss a lot but rarely fool around. Out of the 5 months we've been talking we've only had sex twice. Despite this, both of us have confirmed to each other that we have been having sex with other people throughout our time talking to each other.

After a month of talking, we both were at a party when a guy grabbed her around the waist. I was very drunk and went up and knocked the kids hands away which resulted in her angrily leaving the party and ignoring me for the rest of the night. The next day she said "she can defend herself and what I did reminded her of bed emotions with her ex-boyfriend" I agreed to trust her and let her do her own thing. About two months after that, I brought her to a party where both of us got so drunk that I ended up leaving by myself and leaving her at the place.

The next day I find out she had sex with an acquaintance of mine and at first, did not seem bothered by it. After I confronted her, she broke down and begged for forgiveness and claimed that she "always messes up with good guys". It angered me so much because we literally never really fool around when we hang out, like ever, and ive told her many times that I have physical needs and that we need to start doing stuff more, but nothing has changed.


2.
After giving her the silent treatment the entire day, she texted me at night apologizing and asking to talk to me in person. She ended up coming to the same party as me and kept apologizing over and over and saying how it was a mistake and she really likes me. When she explained her actions (relating to question number 1) , she would say things like oh that guy means nothing to me so sex with him wasn't a big deal, whereas I'm a big deal to her and having sex with me "complicates things" Knowing she was blackout drunk, I figured it would be okay to forgive her, considering we both were having sex with other people and our relationship wasn't "official".

Since then, she proved to me in many ways that she was making effort to keep talking with me such as doing favors for me, inviting me down to the shore and spending the weekend with me, texting me first, etc. Since then, her birthday came around, I sent her flowers, expressed a giant message on how fooling around with other girls is no longer an interest of mine and I want her to be my girl friend.

After all this, she explained to me how "she is sure it will happen soon" but needs more time because of a long-lasting relationship that ended a few weeks before we met. She also said how she feels all of her peers/family think she relys on a boyfriend to be happy and that she needs to confirm that she can be happy as independant before getting back into another relationship. I asked her if could atleast both agree to not see other people and she agreed. After going on vacation for a week, our texts have been getting less and less frequent as she has claimed to be really busy with problems at home and other stuff, but it doesnt seem like her to not want to text all the time.

Addressing both questions, is she even worth all of the effort and work I've put in to trying to make her my girlfriend? I have doubts all the time about if shes being sincere or not but I've never felt this way about a girl in a long time and I would do anything to try to make it work. Also keep in mind throughout the entire time, she claims to "really like me a lot" as do I with her.