Dust mite allergy symptoms

Since my husband was told he has dust mite allergy and should start injection treatment I've been reading online about it.  His symptoms are chronic throat-clearing and coughing which have been going on for years.  He says he coughs and clears his throat because he feels like there's mucus that needs to be expelled.  He doesn't have watery eyes, runny/itchy nose, or sneezing.  I know from other things I've read that his symptoms could be caused by many other problems, but the allergist was the first place his dr recommended.  So what I'm wondering is should he start the treatment?  If it is an allergy that's causing his coughing will we notice improvement right away? He did start using a prescribed nasal spray but while he was at the store he picked up Mucinex too. So he says the cough is better (I haven't noticed yet because we work opposite shifts) but now we don't know if it's the spray or the Mucinex.   He's tried getting an appt with a pulmonary dr but the wait is several months so he doesn't want to put off starting allergy treatment.