Thank you for the additional information.
In a non-smoker, since the symptoms have not improved with the azithromycin (the z-pack is a specific packaging of azithromycin), the primary concern if some tissue has been coughed up is that there is some inflammation of the airway or throat.
Smokers can develop a variety of bacterial infections for which stronger antibiotics may need to be considered, but the germs that cause infections in non-smokers are more limited.
There are a couple of options that can be done to help ease the inflammation. The most effective is the use of a short course of steroids, such as prednisone. An antihistamine
also may help, although it is not as effective as the steroids, but many antihistamines are available over the counter, so have the advantage of something that can be done before seeing the doctor.
If you were having shortness of breath, then it would be more important to be seen urgently for consideration of steroids. But since you are not having any shortness of breath, then it would be OK to try an antihistamine at home initially.
If I can provide any clarification, please let me know.