Had cold: fever, sinus pressure, headache, runny nose. Now still coughing for 1.5 months w mucous. Viral or bacterial infect? Need antibiotics? Which?

See your doc. A lingering cough after an urti can mean a sinus infection or reactive airways, such as asthma. You need to see your doctor to determine what the problem is. An antibiotic should help if there is a sinus infection but will not help if it is asthma.
Sinus infection. 10% of people get a sinus infection after a cold. If the problem has been present for over 1.5 months, you should see your doctor for antibiotic. There are two classes of antibiotics which work well for sinusitis but Z pak (azithromycin) is not one of them. (We are not supposed to provide the name of specific medication on this site)
Needs checked. The possibilities: 1) Lingering cough from previous cold / bronchitis. 2) New viral infection. 3) Bacterial infection superimposed on a viral infection. A doctor needs to examine you to see what's up and what treatment you need.

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