Fighting Fire with Fire
By the sounds of it, you are correct. She is matching her game with yours. The easiest way to counter this is not to try and freeze her out. The best way is to shove your good time right into her face.
Here's what I mean:
Suppose you had plans to go out with the guys, and you invited her along. She tells you no, and you say alright then. Go about with your night, don't text her, and then start up a conversation with her the next day. Tell her how awesome your night was and how you just had the greatest weekend you have had in a while.
Doing this has the effect of building up regret in her. She will see that if she had accepted your plans, she would have had that awesome time too. However, she fought fire with fire and got burned doing so.
Another thing that I'm noticing is that through your description, she may be trying to gain a degree of control over you by trying to outplay you. Don't let this happen. Make her run the conversations, fire up her emotions by randomizing your response time, make her work to get to you.
"There is no better than adversity. Every defeat, every heartbreak, every loss, contains its own seed, its own lesson on how to improve your performance the next time." - Malcolm X