The reason you’re confused, I think, is because you’re the one who isn’t acting straightforward. I know that may sound like a shock to you, and you may even refute it — but before you do, hear me out.
When you met her and asked for her number, you already had a girlfriend and apparently told her so. That’s a mixed message to any woman. But, she gave you her number anyway — [i]because
Her flirting with you in spite of this showed that she liked you as more than a friend, and now you’re not sure why she’s flirting, but still dating someone else (albeit not a “boyfriend”), and going back and forth with you. I think the reason for her flip flopping is due to your initial cue to her that you weren’t one hundred percent into a standard relationship. In your mind you really wanted her, but your behavior showed her that you were only luke warm.
While it may have taken all your courage to ask for her number, she only knows you asked for it while you were with someone else. From her point of view, you could easily be a player. Whether or not you were or are, the reality, from her eyes, is not as clear as it is from your own.
Since that time, 2 and a half months ago, she’s been with a guy who she’s not very serious about (you call him her 2 month guy), and you’ve asked her out twice. This is all pretty normal dating behavior for 2 people who like each other, and are playing the field.
It’s not reasonable for you to expect her to drop all other guys she’s interested in and possibly dating just because you’ve asked her out on two dates in two months. If you really like her, you have to be the one to set the tone for the relationship rather than waiting for her to tell you or act like you’re her boyfriend. If you want to be her “official boyfriend” then you have to do the work to become that — but it’s a process. It’s not something that’s discussed, agreed upon, and enacted, like a business contract. Romantic relationships are a lot less structured. That said, there is a structure to dating that works.
Dial up the dating behavior, and dial down the friend behavior. If you like her as more than a friend, treat her that way: ask her out more often, and spend more face time together and less text time and phone time together. The internet and your cell phone are both great tools for communication, but don’t mistake cyber time for a real, live relationship.
It’s entirely possible that she’s taking her cues from you, and therefore treating your relationship as one that could go either way — friends or lovers.
I hope that helps! Good luck.