I don't have much advice except for suggesting to openly communicate about your feelings. I didn't want to reveal insecurity, and would hold things like this in. I still do once in a while. It was not wise. I ended up making mistakes.
You are not alone. I also have mild social anxiety. Also, I'm poly, but the woman that I'm dating is my only partner. Social outings with larger groups or large parties are the worst for me, unless it is our date night. Then, I feel that it is OK for me to spend most of my time with her at the party. If it is not my date night with her I have a hard time feeling comfortable and at ease in the setting.