Hmmm...she can't stop thinking about you, compares you to others, doesn't think it will work with anyone else...but doesn't want me back. Do you see her confused thinking here?
She doesn't know what she wants. Okay. We can understand her confusion. You are away. She got lonely. She wanted attention. She finds a substitute for you. That substitute guy doesn't take away how she felt about you like she thought he would. Now...what does she do? She has no idea.
Meanwhile, you are away. You won't be back for 4 months. You believe that you can have a long-distance relationship and, if though you might get lonely, you don't go out and find a substitute girlfriend. You are patient, loyal, and are holding on to the relationship.
Is the picture getting clearer here?
You get to choose what you want to do with your life. She gets to choose what she is going to do with her life. It appears that before you left, the two of you made some sort of commitment to uphold the relationship during your absence. You kept that commitment. She hasn't.
Again, each of you has to decide what you want. You have the choice to stay committed to her and, when you come back in 4 months, to see if you can pick up the pieces. Or, you can say forget it, I'm not waiting for her. She also gets to make choices here as to how she wants to handle this.
Clearly she doesn't know what she wants. Are you willing to give her the room to figure this out? Or, have you had enough?
It would be easy for you to say...she's out dating...then so should I. However, I would caution you not to make a rash decision like that. If you truly believe that you want to mend this relationship on your return, then be extremely careful in how you proceed. You certainly do not want to add more turmoil on to the situation.
I hope this helps.