Hi.. Welcome to HEALTHCARE MAGIC.. As per your complain pus discharge from the nostril and bad breath after surgery to remove tooth piece from sinus clearly indicates that you have infection in the sinus due to aspiration of tooth piece into the sinus leading to pus discharge and bad smell as the sinuses drain through nostrils.. I would suggest you to consult an Otolaryngologist and get evaluated and a thorough clinical evaluation and investigations like PNS view x ray or MRI scan can help in diagnosis and treatment can be done accordingly.. You can be advised a course of antibiotics, anti-inflammatory painkiller like Ibuprofen, decongestants like Pseudoephadrine, do saline nasal irrigation, steam inhalation and use a humidifier in your room.. You can also be advised decongestant nasal sprays containing Xylometazoline or Oxymetazoline.. Avoid spicy and chilled foods.. Do warm compresses around nostrils.. In case if the condition doe not recover then Endoscopic sinus surgery can be advised.. Hope this helps.. Regards.