@Joe123,
I'm getting the feeling you haven't had a lot of relationships.
Be that as it may, you were both drunk, so who knows? You have her number, right? And you know when she's returning from Turkey, right? So live your life and then call her when she returns. The following are possible scenarios -
1) She's broken up with the other fellow and wants to go out with you.
2) She's broken up with him but does not want to go out with you.
3) She's still with the other fellow and does not want to go out with you.
4) She's still with the other fellow and wants to cheat on him with you.
5) She wonders who the heck you are and how come you have her number, and/or why you are asking her out.
As for the likelihood of each of these, I'd say #5 is the least likely, but you never know, what is said while drunk is often forgotten later. Or it is conveniently forgotten.
In the meantime, she is going on vacation with this other guy. Chances are extremely good that a room will be shared somewhere in there. You have no claim on this woman whatsoever. You have no real right to jealousy here if it turns out she isn't broken up at all.
Live your life. Call when she gets back, if you want to. But do not sit around waiting, hoping that all will be smooth sailing when she returns. I am willing to lay down money that it won't be, sorry.