Please Help, Am I Doing The Right Thing?

Me and this girl met when we were 15 &16 ( me older ). I felt like I fell in love with the girl when I first saw her. Things were great the first couple months. Then I started noticing some major anger, her fighting with her family, very harshly too. I also started hearing things about her being kinda flirty, and has been with a few people, and keep in mind she is 15, a freshman in high school. Then I started to notice more kinda flirty attitude around guys. I didn't like it at all but didn't say anything for a while. She texted a lot of guy friends too. We got into a lot of fights and broke up and got back together multiple times over the 10 months. We finally broke up for what I thought was the final time. We were apart but tried hanging out a few times every couple months or so. It never really worked, for me. She thought it was great every time. Also EVERY time we would break up, she'd be out dating INSTANTLY. And she bounced from her ex boyfriend to me 4 times in 2 weeks! I stole her from him every time. Just to see if she is actually that immature to go out with someone when you still have feelings for someone else, that's so rotten. And One month ago exactly we tried again ( now 16 & 17 ), I thought it was good for a while, then I just couldn't get over all she has done. She has never cheated to my knowledge. She just talks to and texts a lot of her ex's or people she has done stuff with. She just doesn't stop either. So pretty much I'm unhappy in this relationship because she lied to me a lot in the beginning & I felt like she hid a lot of things from me including all the people she's been with and she even went and hung out with her ex's before without me! I think I still feel something after so long because I fell in love with her after I found out all of these things. So I broke up with her tonight. Please I just want opinions. Sorry for the long post. Thank you!