Usually coughing is one of many asthmatic symptoms that occur during an asthmatic episode.
Either way, coughing is very normal for a recent non-smoker. Tar deposits and phlegm are breaking up inside your lungs, and your lungs start regenerating new cilia and linings.....
If you are exercising also, then mild coughing could be normal, as your lungs and heart are being pushed to work harder than they are used to...
Unless your coughing is out of control, makes your asthmatic, or you cough up blood spitule, don't worry too much....