Everyone may have a different opinion on this subject, but here's my opinion:
You're not over using <div>.
If you were using <div> when you should be using <h2>, <p>, etc, then you would certainly be doing it wrong. In other words, if you're bending <div> to fit your every purpose, you've got a problem.
Unfortunately, when CSS started to get popular, there were a lot of articles written promoting this practice with titles/themes following a "Use <div> instead of <tagX>!" pattern.