Have you tried the Neil Med sinus rinses, and mucinex helps too.
Hot steamy moisture penetrates the sinuses.
You might have a sinus infection like I do.
If the cough is primarily in your throat, no lung congestion really and you have pressure, feel achey, have bad breath and a nasty taste in your mouth, extremely gross nasal secretions with blood or puss, you may need an antibiotic.
Sinus infections can trigger asthma and can turn into chest infections too. In extreme cases they can cause brain infection! Even if sometimes the mucus is clear, it can just be filtering past the nest of bacteria up in your sinuses.
A few days in on an antibiotic and all that horrible stuff starts to drain out.
Nasty, nasty illness. :-P