I have to say, at a first glance, she doesn't sound very supportive of you. While I can fully understand the need to be herself and express herself, that doesn't give her the right to tromp all over you.
You said he came over, so I'm assuming you and she live together. That makes it your home as much as hers, and as such, you have the right to some boundaries within your own home. Sharing a house with someone means you can't just do whatever you want all the time. You have to respect your housemates' boundaries, or it ain't gonna work. You have the right not to walk into your living room and see your partner making out with some dude on your couch. That was a pretty selfish and insensitive move on her part.
I have to ask: is it really worth it? She isn't being supportive or compassionate, and it doesn't sound like this mono/poly thing would be your first choice for a relationship dynamic. Words like "clingy" and "burdened" indicate that she isn't likely to become supportive any time soon. It sounds like she's only interested in a relationship that is trouble-free, easy-going, and uncomplicated. It doesn't sound like this relationship is ever going to be like that.
You can't "make her happy." Only she can do that. And the flip side of that is only she can make herself unhappy. If your mood is bringing her down, then she could choose a different way to react.
Right now, it sounds like you're sacrificing your own happiness in an attempt to fulfill hers. That's going to tear you apart piece by piece until you're nothing but an empty shell. So if what you want is monogamy, then it may be time to admit that you and her have different ideal relationships and that this arrangement cannot fulfill both of you.
“As I am sure any cat owner will be able to tell you,
someone else putting you in a box is entirely different
from getting into a box yourself.” —bisexualbaker