<human>: Could you distill the essence of the text into 1-3 sentences?

A bit of background. We've been together for 3.5 wonderful years. I love him dearly and for so long it seemed nothing he could do would make me unhappy. Until now.
At the beginning, we mutually agreed (no coercion or compromise) that an open relationship would be ideal with us, and we'd disclose everything to one another. In that time I've slept with about 6 different people and he's kissed and fooled around with 2. That was all fine with me, until recently he met a girl on a dating site, and started having sex with her.
I knew that extramarital sex would be the inevitable and I thought I would be okay with it. He always seemed at ease when I told him about what I'd done outside of our relationship, but I can't seem to feel the same way. When he's with her, I feel sick. He has spent the night once or twice and I laid awake all night shaking, crying, and being unable to sleep, thinking of all the things he was doing with her. I have (gently) discussed with him that I feel awful about him doing it, but I'm not interested in changing the terms of our romantic agreement.
I should add, his sexual interactions with the other girl are rare-ish (once every 1-2 weeks) and he almost always comes home to me. I have no doubt that he loves and wants to be with me. But it still makes me feel so insecure and so awful and I can't seem to change my obsessive thoughts about it. It's at the point where our relationship is suffering because when he touches me I just want to cry.
I honestly do think an open relationship is ideal and I'd never agree to monogamy (I'm 90% sure I'd end up cheating). What do I do about all these feelings? Does anyone else have experience on this subject?
<bot>: My boyfriend has been having sex outside our open relationship.  Changing the rules of the game is not an option and I don't feel like we should break up.  How can I handle this/my feelings?