You probably have a chronic sinusitis and you may need antibiotics to clear this. Also rinse your nose with salt water ( 1 cup boiled cooled down water - body temperature - with 1/2 teaspoon salt) sniff it up and blow it out until the water comes out clear. The things you cough up, are called tonsilliths and are calcified debris from the tonsil crypts. Try gargling with salt water to get rid of it.
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