Hi.. Welcome to HEALTHCARE MAGIC.. I have gone through your query and can understand your concern. As per your complain and presentation of symptoms coughing up white stinking particles seems to be TONSIL STONES or TONSILLOLITHS which are formed due to calcification of food and dust debris over the tonsillar crypts leading to formation of small bad smelling stones.. Nothing to worry and you can remove them using a q-tip gently and to prevent them from forming again maintain a good oral hygiene.Do warm saline gargles twice a day.. Always gargle after meals.. Limit the intake of milk and dairy products as they contain more calcium and will increase the chances of stone formation.. Use an antimicrobial mouthwash to gargle Drink plenty of water. In case if manual removal is not possible consult an ENT and get evaluated and he can remove them but if the formation is not reduced and it causes recurring tonsil infections and bad breath then many a times Tonsillectomy that is surgical removal of tonsils is advises.. Hope this information helps.. Thanks and regards.. Dr.Honey Nandwani Arora.