I read your definition, and thought, "Yeah, I'm an introvert because I like to recharge alone." But then my next thought was, "Actually, it depends on how I'm feeling." Often I seek company because I like to recharge with other people.
Am I an extrovert or introvert? I don't feel like I'm in one or the other for the particular majority of time. I don't believe it's a great model for describing everyone.
For the record, I used to be shy but forced myself out of it. I also felt I had to learn new skills (sometimes a painful process), but I still don't believe I'm naturally either introverted or extroverted - neither really describe me or my behaviour.