Get a foot massage before the party. Before my last big exam, I had a foot massage from noon to 1, lunch from 1 till 1:20-ish, and the exam at 2PM. I arrived at the exam site about 15 minutes earlier and just walked around. I passed the test, and it was a hard test. All that work soothing my nerves - a foot massage, eating, walking outdoors - must have helped me. Plus, for me with my former habit of being perpetually late, every time I arrive earlier is a confidence boost and a relief from anxiety.
With the party, coming earlier does not make sense - it is not an exam - but coming in the middle of the party would cause more anxiety than coming in the beginning, I would think, because when you come fairly early, it is as if you were kind of like a semi-hostess and the newer people would be for you to greet, whereas if you come late, you'd feel thrown into the midst of its all. So I would come 15 minutes after the official start of the party.
I absolutely cannot wear heels. If you do wear heels but are not VERY comfortable in them, then don't wear them - they would just cause you more stress and discomfort.
If you are a little superstitious

, wear some jewelry that has meaning to you, as a protective amulet

.
Most importantly, remember that it is not YOU AGAINST THEM. It is not you, the only socially anxious person, against a bunch of gregarious "life of the party" types. People would be everywhere on the spectrum, and some, as socially anxious as you are.