I suspect I do. I have been on anxiety and depression meds for 15 years after being diagnosed with GAD. I recently started looking into my social issues and took a bunch of online personality tests and all of them scored me high for schizoid personality disorder. I had no idea what a Schizoid was, but the more I read about it the more I saw how I fit the profile. The anxiety is part of it, but when you add all the social and emotional aspects you may find it's something deeper. Schizoid sounds like you must have some eff'ed-up problem, but from my research it's not that uncommon.
Have you done much reading on it? Don't think of it as another "problem" in addition to anxiety - think of it as a classification of your personality that explains your anxiety.