How can I stop being socially awkward?

I am VERY introverted and will not talk to people unless I genuinely have to. I can never look a person in the eye and when I do talk I look at their feet not their faces. It's starting to get on my parents' last nerves on how I do everything I can to avoid social situations and when I'm around people I start sweating and I feel hot all over my head and start to feel dizzy. I know I can't avoid them forever but I'm just terrified of even being judged because I'll admit I'm very clumsy and also have trouble paying attention so when I'm listening I rarely can follow along with a conversation. I don't mind being alone (I'm used to it after all) but there are times I wish I could have more friends. I have about 1 to 3. My parents also constantly compare me to my sister (who is a social butterfly) they tell me to stop acting this way and I really am trying but I've had this problem since I was little. I can practically feel this harsh and pitiful looks people give me and it really makes me uncomfortable. So basically...help! What is wrong with me? How can I stop this?