I think this girl I like is talking to a lot of other guys? What would you do?

So I met this girl in June and we've been tialking on and off a lot and she says she likes me a lot and I like her. I want to get close to her but I ignore her sometimes becuase I see her calling guys "babe" and putting hearts around other guys on snap chat. A few weeks ago she put this pic of this guy and I didn't hear from her for a week and she comes out and says she misses me. I ignored her but gave in the next day and started talking to her. Last week she didn't reply to me and put a heart around this dude on snap and did it to another guy a few days later. She was wondering why I wasn't texting her and I was ignoring her again. I wasn't gonna forgive her this time but she came to my work and I couldn't help it. So I'm talking to her again and she's telling me I'm her one and only. I want to believe her but I'm not sure I do, I have a lot of feelings for her and she tells me she does too. I want her to be mine but I feel like she is running around with other guys all the time:( what would you do?