you must be having severe bacterial infection of the pharynx. as your taking z pack, that will take care of infection. but symptomatic treatment is also essential, take analgesic
and decongestants. also do warm saline gargling at least three times a day. since tonsils are swollen, that may be causing obstruction to liquid, and hence going to nose or if this is diphtheria
of pharyngeal muscle may cause this symptom.
wish you good health.