The gap between the class and the social floor is where most people freeze. In class you have structure, a rotation, a teacher; on the social floor you have to walk up to a stranger and ask, then hold a wordless conversation for four minutes in front of everyone. It is genuinely frightening, and pretending otherwise helps nobody.
The first thing worth knowing is that nearly every confident dancer in the room felt exactly the same once. Social dancing looks effortless from the outside precisely because everyone has been through the fear and out the other side. You are not uniquely nervous; you are at a stage everyone passes through.
The way through is to shrink the task. Do not aim to dance brilliantly; aim to have one friendly, low-stakes dance, ideally with a beginner or a kind regular who will not mind your nerves. Tell them you are new. Almost universally, experienced dancers respond to that with warmth, because they remember, and because a happy beginner is the lifeblood of a scene.
Lower your standards for the first dozen dances on purpose. Basic step, a couple of simple turns, a smile, a thank you. That is a complete, successful social dance, and stacking up a few of them quietly dissolves the fear far faster than waiting until you feel ready — a feeling that, if you wait for it, never quite arrives.
Then keep showing up. Confidence on the floor is not a personality trait you either have or lack; it is a residue that builds from repetition. Six weeks of turning up and having a few small dances will change you more than any amount of practice at home. The only real trick is to keep walking back in.