If your mom has sinus problems the cough could very well be from that especially if she is doing alot of coughing when she lays down. The mucus drains down the back of the throat and irritates it. Post nasal drip can be a trigger for people with asthma too as it is that irritating. Years ago I had alot of these issues with post nasal drip then I asked my doctor for a nasal steroid inhaler and it helped to the point where I no longer had any problems and weaned myself off of it after two years and due to the fact I now eat a diet that is very anti inflammatory I have had no problems for the past 4 years!
Coughing can be the sign of alot of things, yes lung cancer is one, lymphoma is another as my friend that had Hodgkins lymphoma went to the doctor because of a cough, he gave her antibiotics. I told her I would not take antibiotics unless he showed me an x-ray that showed a pneumonia since that was what he was thinking she may have, she went back demanded an x-ray and there was a huge mass wrapped around her heart, turned out to be hodgkins lymphoma she did her chemo and radiation and has been cancer free for over 1.5 yrs now
Other reasons for coughs are allergies, COPD,some medications, other masses in the lung be they TB or cocci or any other of the fungus problems. It could be something as simple as something in the air that causes an inflammation in her airways or it could even be heart related. Cough is the symptom of so many things.
The throat clearing thing would make me think it is sinus related or something in the upper airway or pharynx causing the problem. Back when I had problems I had caught a virus that inflammed the uvula ( the thing the hangs down in the back of our throats) and it made it swell so it was longer and touching the part below it and it made me cough like crazy and clear my throat all the time as it felt like a huge glob of mucus sitting there.
Maybe your mom is afraid but if that it why she does not push harder to find the cause she needs to understand that even the worst of these problems can often be cured when caught early so ignoring the cough could cost her her life if it was some form of cancer and on the flip side if it is one of the lesser evils such as I had, within days it could be gone with treatment and life is SO much nicer without an annoying cough and post sinus drip!
Hope this helps. Good luck, JanMarie