It is not uncommon for people to cough more after quitting. I am going to a few links below that explain why it is a pretty common reaction. At the same time though, coughs should not be ignored and symptoms should not be indefinitely written off to simply not smoking. I will attach a few links addressing this issue too.
I had a question emailed to me about throat clearing at four months. Coughing and throat clearing can go on for months after quitting. It is best to get checked out by a doctor to make sure nothing else is going on, but if checked out and all appears to be clear, it is fully possible that the extra throat clearing and little cough can still be the cleansing effect from having stopped smoking.
This is probably the most often asked question I get via email to the AskJoel site. Since I started this thread I have made a number of new videos that covers this topic. Here are links to the videos that discuss smoking's impact on the lungs and the repairs that occur after a person quits.