I'd definitely get it checked out, as not to alarm you, but coughing could be a sign of heart disease, as we learned with my parent's dog. My dog has had hacking at times, for which she simply had an infection, and after antibiotics, it went away. Came back a year later, and the antibiotics took care of it once again. Best a vet takes a look. Good luck!
A hacking up a hairball type noise makes me think fluid/phlem )spelling, yikes). Reverse sneezing is more of a honking noise, the dog will arch their back and suck in their stomache very deeply and 'honk'
This is something you have to hear to guess honestly. Be safe...let the vet take a listen. It could be as simple as reverse sneezing or something in thier throat tickling them to bronchitis/pneumonia or even CHF.
Better to nip it in the bud as early as possible in case it is something more involved:)
Keep us posted.
Life isn't about waiting for the storm to pass. It is about learning to dance in the rain.