Terrible at Social Interactions... What should I do?

I am God-awful at meeting new people in a social setting (I do much better in a professional setting). I never know what to say when someone just comes up to me and says, "What's your name?", and stick out their hand. My mind asks me, "Why does this stranger need to know my name? What are they up to?", so there's a pause before I quietly tell them my name and ask what theirs is. I don't really care what their name is, but I understand that this is how polite conversation works. I never know at which point I'm supposed to shake their hand. It seems odd to do it while talking and listening, but awkward to leave them hanging. Plus, I really don't like touching strangers or having them touch me, so it's an effort to force myself to do it.
Also, with people I know casually, I never know whether I'm supposed to shake their hand when I see them or hug them or what? Whichever way I go it always feels forced and robotic.
My husband is a sound engineer in the local music scene, and I meet a lot of new people through him. People he already knows well and I know about, but haven't met yet. I know that my social ineptitude reflects upon him, so I really try my very best, but when I do something that feels clumsy, it puts me in a state of near-panic.
Since I'm a musician as well, I find that once we get past a few awkward introductions, I'm able to be a little more relaxed, but then I often find myself talking TOO much. I don't mean to, but I feel like it's some kind of conversational imperative to fill in the quiet spaces, I guess? By the time it becomes obvious to me that I'm hogging the conversation or that they're getting bored with it, I don't know how to end gracefully, often simply stopping abruptly or even walking away out of embarrassment. It is a real handicap and I need to know how to fix it!
I am 43 years old. My mother was quite anti-social when I was a child. She never had company that wasn't a relative, and didn't talk to any of the neighbors except for the man across the street who cut our hair. She didn't make friends with any of our friends' parents unless they were on a Girl Scout committee together, and even then, it was mostly a business-type friendship. My father really didn't have time for socializing. He was gone in the Navy until I was 4, the worked the night shift, attended school during the day, and slept most of the hours that he was home up until he graduated when I was 12. Shortly thereafter, but youngest sister arrived and all their time (and ours) was consumed with taking care of her, so I think I just missed out on being properly socialized.
I was quite active in band in school and met a lot of intramural kids that way and was friends with the other kids in our neighborhood for the most part, playing kick the can and ghost in the graveyard and building forts in the woods with them. It was a small island community so the kids were more like nomadic siblings than friends. I think I got along alright back then, but now I feel so out of place everywhere I go. I'm not sure when things changed, but I always feel so inferior to people and I wonder what they're trying to trick me into. I've been incredibly naive in my lifetime and have gotten fooled so many times by molesters and abuser that I simply don't trust my own discernment. It takes me a long time to trust anyone, and if they betray me once I do, it gets harder and harder to recover each time. Does anyone else understand this?
I really want to have a functional life. I work well below my level of ability simply because I'm too afraid of being tricked and embarrassed to even try to fit in with my intellectual equals. It pains me that I'm academically gifted, but socially retarded. And I just don't know what to do. Does anyone have advice for me?

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Read Navigating the Social World. I know, it's a book for autistics, but it gives great advice for anyone.

Thanks so much. I will look for it immediately

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I've felt just like you described every time I go to some social event. Unfortunately, I use the "that happened to me, it was...." And people get tired of that quickly. I get panicked and have to use my xanex just to get me out of the house. Like you, I remember being normally sociable, but once my bipolar disorder took over my life it brought this social panic with it. It even affects me going to group support groups. "What I am going to do to try to address this in a positive way" is to take a look at the book that the previous poster recommended. I've been told to use the xanex and after I have a number of positive social events, my fear will decrease. So far that has not happened for me after about a year. Know you aren't alone, and three are many like this who are afraid to even post on a social site. Choose a positive thing to do, even if it isn't directly related to the problem. You'll feel better. These are my own thoughts and may not work for you, but id wish for you that you find something that will give you a positive hopeful feeling. Blessings to you, mtnannie