I suspect this is very common, if not typical. Your family is the first social interaction you ever have, and the only one that really survives even in the absence of normal social relations. You can coast along easily in a family that barely communicates at all, where other relationships can fade away and be forgotten. This isn't really good for anyone involved, but it happens all the time for various reasons.
Remember, your anxiety comes from within you, it's not something that's inherent in all social interaction. Just because you "should", ideally, have a certain kind of communication with your family, that doesn't mean your particular family situation was conducive to that. Poor communication in the family is a major cause of many people's social anxiety initially.
Even if your parents didn't have any overt negative effects on you, just lack of communication can make you grow up feeling insecure and uninteresting and all the other things we so often feel. And until you get a bit older, it's hard to tell whether your family is like everybody else's, and whether it's really fair for you to be judging yourself based on what other people's families are like.
The truth is your family is yours alone, and even if it isn't ideal, it isn't just your fault for not having it the way you wish it were.