The anxiety that I'm experiencing (I never say 'my' anxiety as to claim ownership of it) isn't as bad as you describe. I can maintain a job, drive, go shopping, and go pretty much anywhere else in public. In short, I can get out of the house like most other people. However, it doesn't mean I don't experience any anxiety when I do these things. For example, sometimes I feel anxiety at the check-out counter when shopping.
Anxiety sometimes causes me to rub people the wrong way. Like at my job I have right now, a coworker wanted to fight me and then ended up quitting because of how he perceived my stand-offish behavior. I know it's because I just came off cold to him since he was a high-energy, high-social person who was always trying to talk to me and I have been more low-energy and shy. Thus, I wouldn't reciprocate his interest and I came off a little bit unfriendly, but of course he didn't know the truth. I didn't talk to him much simply because I don't know what to say a lot of the time.
Also, sometimes when I make eye contact with people it comes off as hostile or weird because it just makes me uncomfortable. So, because of my behavior, he's not the only one at my job who thinks I'm weird or mean (though I talk a little bit to some people there who think I'm a nice guy). Anxiety causes difficulties, but I have to work. I have to have a job so there's really choice but for me to go to work. I'm glad I have a job that at least forces me to be a little bit social. It's in a restaurant environment. I interviewed for a waiter position at first and I didn't get that because I think my manager obviously saw the lack of social skills or shyness. Might've been too much for me at the time anyway.
I'd definitely agree with what a poster above said about social skills being important for succeeding in your career. Obviously, you can do well without social skills in a job like computer programming, but social skills are a bonus for any job. The more likeable you are to people, the more they want to help you and see you succeed. You have a better chance of promotion, for example. With social anxiety, obviously people tend to not like you as much. And if they don't dislike you, at best they're neutral towards you, meaning they don't have much of an opinion of you other than maybe you're quiet. I'm not saying this is always the case, but oftentimes it is.
