I am only open to monogamy but that doesn't mean I'd consider my partner property. I don't get why you said that.

I'm sorry you're going through this. Maybe self soothing yourself in healthy ways and CBT. She is doing an act of love for you by offering not to see anyone. You don't want to be "selfish" but what's wrong with caring for yourself, and believing your partner when she says that its ok? or break up / take a break. That's also an option too.

Best wishes.