What is the cause of dry cough?
Cough-variant asthma is a common cause for a non-productive dry cough.  Asthma is not a single condition involving bronchospasm and with associated wheezing - there is a variant that is primarily or only coughing.  

There are different inciting factors that bring on symptoms cough-variant asthma.  Most commonly they are exercise-induced, cold-induced, allergy-induced, or quite commonly it happens following a viral respiratory infection (post-viral-URI).  Symptoms can be acute (exercise or cold) lasting minutes, or chronic lasting days-weeks or even indefinitely.

The pathophysiology for each is different.  The latter 2 are inflammatory processes, as you mentioned, each a little different (hypersensitivity versus residual infectious inflammation).  I am a little uncertain about the mechanisms you described, and I am not sure the correct thing to focus on is scarring.  I would focus primarily on the inflammation.  Inflamed mucous membranes are extremely sensitive, reacting to even dry or cold air.

Using a long-term steroid inhaler is a preferred method of handling chronic cough-variant asthma, as it reduces airway inflammation.

There can be other causes of cough such as postnasal drip, chronic rhinitis, sinusitis, or gastroesophageal reflux disease (GERD or heartburn).