Nothing wrong with sweating or talking silly, it happens to everyone, even public speakers and political figures. You're not the only person to go through that. I get somewhat nervous when I speak to certain people I'm not familiar with, sometimes I may trip over a word or two, but it diminishes as I spend more time with the person and start feeling comfortable. All people are anxious to some degree, worried about what others may think etc.
You don't have to be a social butterfly, I am not. I am very introverted and very much a loner, but at the same time, I force myself to get out of my comfort zone on occasion, especially if it's something that can affect my daughter -- I don't want to ruin her fun by making her stay home because I don't know anyone at a party. I sometimes end up being a sideliner, watching everything and barely muttering a greeting and that is okay, or I find someone I click with and end up spending the evening chatting with that person.
Don't be too hard on yourself if you weren't able to find anyone you clicked with. We all have those days, just don't give up and don't be so hard on yourself. Do realize that a lot of people are feeling the same way as you and cannot be bothered to realize if you're sweating or stuttering -- they probably are doing the same thing and in their own little world fretting over that. As soon as you start feeling more secure and less conscious, you'll be able to relax more and just go with the flow. Believe it or not, most therapists believe in exposure therapy, which means gradually facing your fears, so they'd probably advise you to do something similar to what I advised.