Alright my friend. Take a breath, relax and know that whatever happens was meant to.
Now, take a good read through the information at this link. It should provide some clarification as to the difference in Poly and cheating. Read the rest of it too...It's gentle and an easy read.
Next, accept the simple truth that "not telling you" about a boyfriend/girlfriend/one night stand is cheating. The common thread in all approaches to poly seems to be honesty and openness before
If she's using the word poly to explain her approach towards hidden relationships, she is bastardizing the word.
I feel for you brother and hope you can find a way to nurture the love you have for her. But do not put yourself into a situation where you are miserable in all but the moments you have together. That is no way to live.
Peace and Love