Should I be concerned?

Any bad cough that is nagging and persistent should be checked out. A bad cough as you explained could mean you have anything ranging from an allergy to serious throat malignancies. Therefore, it is important to have a professional look at it for you. I would not suggest referring to sites such as: webMD or the like. Those sites can only scare you. Should you be concerned? Yes and no. Like I said, the cough could be nothing or, it could be something you need to get treated for. Only the doc can tell you. :)