Anyway should I call her out that she seems to be lying?
Yes. You should do exactly that if you do not want to have any more contact with this girl.
I agree that she very well might just be busy. But continously breaking plans is disrespectful. And THAT is the thing you should be upset about, not about her being busy.
The more and more I attempt to get with this girl the less and less I find my self interested.
Well, I think you solved your own question then...
The problem with me right now is I don't want to let her go to early because it could be a huge mistake.
But you don't have her right now to let her go.
Do this - stop thinking about her. Expand your social circle and look into other potential dating partners. Let other people and things be your focus. Basically, you get busy for a while.
If she suggests another meetup and you want to go, then go. But don't make it the main priority for you.
Good luck.
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