Ablexi, this is a case where I really wouldn't feel like I had a relationship if I were you - you've never even met! You say you've been "together" for four months, but - no, in actuality, you haven't been together. You've only been communicating long-distance, and she's found someone local. It's not a matter of trust, it's a matter of getting to know someone, and four months is a tiny blip of time. It's nothing, you're just starting out. So, let it be casual for a while until you really know for sure, and then decide if you want exclusivity or not. And meet her as soon as you can, for goodness sakes!
I couldn't consider someone a boyfriend without ever having met him and interacted with him in person, over time. Up until a face-to-face, everything about the "relationship" is just a maybe. Perhaps she feels the same way.
The only kinds of LDRs I can do would be if we could meet in person at least once a month, or every other month at the most. Less than that and it wouldn't feel like a relationship to me (of course, it's understandable if there are moves, deployments, etc., after a relationship has already been established in person). I need quality face time for it to be considered serious. Being apart for long periods isn't so farfetched if you're poly, but some people live with that and that's the only relationship they have!
Independent solo polyamorist seeking lover-friends willing to invest in friendship, companionship, and love, but without a need for partnership.
Never confuse commitment with exclusivity, love with ownership, nor sex with intimacy!
For me, it is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring.
~ Carl Sagan