The first thing you HAVE to do is calm down. You've got social anxiety so you're gunna be anxious. You have to fight the first crippling wave of 'I want to go home'. What I always do is act like my actions will have no affect on tommorrow, like I'm never going to see these people again. Especially in front of crowds with speeches, I just have to think 'alright, I will never interact with them again'. During a party, try and scope out something that might be interesting or someone. The best bet it to go for the people on the outskirts like you. Approaching a group is difficult and piercing their group dynamic is hard. If all else fails in a social event, politely excuse yourself to a quiet location and from there formulate a new strategy.