Bronchitis or asthma

I'm not sure what I have.  Two months ago I was diagnosed with bronchitis (no chest xray was done).  I was given antibiotics and started getting better.  Now I have this dry short annoying cough that at times is rough sounding, it doesn't feel like something wants to come up.  My chest feels uncomfortable like when you breathe in cold air and need to cough. I have been very sleepy this week.  Every morning my head is congested and at times I feel short of breath.  I work out 3 times a week, sometimes I'm fine and other times i feel dizzy.  

A year ago I had bronchitis, and 2 1/2 yrs ago I had pneumonia.  I have a history of wheezing when i inhale only.  it is very minimal and have never seen a doctor about it.  I have never smoked.

Is this a typical pattern of bronchitis or do i have chronic bronchitis or perhaps a certain type of asthma?  Your input is greatly appreciated.  Thank you.  Amas

[National Jewish Health]

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.