It doesn’t seem likely that belching and sinus drainage are connected.
Constant sinus drainage is probably due to some chronic sinus infection (chronic sinusitis). Chronic sinusitis is usually due to an uncured infection, allergy or both. Nasal septum deviation (congenital or acquired) can make mucus drainage difficult and sinuses more susceptible for developing infections. An X-ray image of the para-nasal sinuses may confirm or exclude nasal septum deviation. A sample from the nose and throat for microbiological examination may need to be taken in order to choose a proper antibiotic if bacterial infection is confirmed.
Treatment usually includes proper antibiotic, corticosteroids and infra-red irradiation of the sinus area on the face. If there is nasal septum deviation you may need surgical treatment.
Belching is usually caused by drinking and eating too fast, drinking carbonated drinks (coke, beer, champagne) or talking while eating. Changing your eating manners may help you stop belching.
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