The recovery state of acute bronchitis can be characterized by a chronic cough that may last 3 to 6 months. However, such a cough may also be a sign of underlying asthma, with the acute bronchitis superimposed on the asthma, even if you have never been diagnosed with asthma.
Asthma is not usually characterized by wheezing with inhalation. Such sounds with inspiration suggest an upper airway obstruction, not infrequently a problem with one's vocal cords, either a weak or paralyzed vocal cord or a condition called vocal cord dysfunction (VCD). You should ask to be checked for both asthma and VCD.
Chronic bronchitis is characterized by daily productive cough, with no other discernible medical cause, for more than 50 percent of the time over a 2 year period, and is associated with recurrent bouts of acute bronchitis.
All of the above are worsened considerably by cigarette smoking.