Monogamy is a loaded noun. It can mean different things to different people, particularly when many miles separate you. 

A friend of mine once thought her and her LD boyfriend were monogamous, only to find out he thought he could sleep with whomever he wanted as long as he didn't talk about it. "Don't ask, don't tell" or "What happen in LDR's, stays in LDR's, right?" Um, yeah. Needless to say, things didn't work out between them.

To avoid this painful scenario, talk about what you expect commitment-wise from one another. Is all physical and emotional contact with the opposite sex off limits? Is kissing okay, but not sex? Define monogamy and all of its terms.

If you find you've both been having difficulty controlling your impulses, you might be able to agree on some sort of semi-committed scenario that works. Or, you might not agree, and decide not to move forward. But, you will never know what your true feelings and possible options are until you discuss it.