wait, so when you were drinking you didn't have the cough?
Here is a thought, some thing in the past was damping down the cough, for example pain pills like vicodin can kill the urge to cough.
perhaps booze was doing this for you. it was suppressing the urge to cough
and YOU quit the booze so now there is nothing stopping the cough
the cough is from irritations for many years. it has been stopped from something you were taking, drinking or eating for many years
now I'm not saying you should start drinking again. maybe take a spoonful of honey.
I know someone who didn't cough, started using pain pills, quit and started coughing. It sort of re arranges your cough tolerance level.
I AM NOT A DOCTOR, but play one on tv