Constant throat coughing

I had a cold but now have a constant throat coughing for 4 weeks/not in my chest/ and my throat is a little red/ I have gargled with warm salt water - and what I cough up is clear, no fever, is this sinus drainage?  I can breathe through my nose with no problem - not stuffy.  Otherwise I feel great - little fatique but nothing else.  What is this and do you think it is serious enough for me to see a doctor?

[National Jewish Health]

A persistent cough following an upper respiratory infection is quite common, but the great majority of such coughs resolve spontaneously within 12 weeks.  The cough could be from sinus drainage, from infection precipitated asthma or from residual inflammation of your nose and/or sinuses from the "cold."  If the cough persists for more than 12 weeks or if you develop any other respiratory symptoms, then you should see your doctor.  Otherwise you would not need to see your doctor.