Hi Anacrusis,
My wife had a never ending coughing problem 3 years ago which took 6 months to get DX thanks to an obstinate pneumologist and the outcome of a battery of tests unfortunately was "lung cancer" ...in her case, a relapse from a breast cancer treated 20 years ago!
Also in her case, the coughing problem was associated with persistant tiredness.
So don't mess around and see a competent pneumologist ASAP!
I hope you'll get a reassuring answer,
Maurice.