I don't think you're being controlling at all. I think she was making you feel suspiscious of her actions and all you did was confirm what your instinct was already telling you. It doesn't seem like she's given you a reason to trust her!
At the same time, if you guys were broke up when she slept with these other guys, then you shouldn't hold that against her. She had the freedom to do whatever she wanted to do - as well as you had the freedom to do what you wanted to do.
She probably lies to you because she does care about you and she just doesn't want to hurt you. I don't think she understands that, sometimes, it hurts worse when someone hides something or lies to us than it does if they were to just come out and tell the truth. Plus, she's just starting her life. She's trying new things and she's probably wanting to explore a little bit.
I'm not going to sit here and say that you're not in love with her, because you very well might be. I think you guys need to do some serious talking and learn to trust one another. Mistakes happen in every relationship, it's pretty much inevitable. But, being able to work through those mistakes and learn the lessons being taught?! - then that would make your relationship stronger. I think you've got some serious soul searching you gotta do.
Good luck! :-)