You don't have horrible social skills. Your first post demonstrates that by showing that you understand the principles of social interaction and how your actions can make others feel. Doing that requires social skills, the ability to empathise, that sort of thing.
What you could use more of is
self confidence. Of course it never hurts to study
social skills either since they tend to influence each other strongly.
You're assuming the negative about yourself and other people (especially what other people think about you) and you're overestimating the negative consequences of an awkward conversational misstep. You're not getting caught doing the CEO's wife on his desk, you're making a minor slip in conversation. Unless you hit a huge freudian slip odds are nobody will remember even days later if you dont make a big deal out of it.
I know how you feel Soma, I literally had next to no human interaction from about the 5th grade until my junior year of highschool, and even then it was pretty sparse. You can learn to be better in public and with people, self-confidence is a muscle. The more you exercise it the better you'll get. Just remember to not let things get to you, especially not in the long term, and you'll build some resiliency too that will make your mistakes feel like they sting a lot less.