Hi..
Thanks for the query..
I have gone through your query and can understand your concern.
As per your complain and presentation of symptoms the white smelly things that you have over the tonsils that are smelly and are coughed up are calcified structures known as TONSILLOLITHS or TONSIL STONES.
They are formed when food particles and debris gets deposited over the tonsil crypts and gets calcified and are bad smelling structures..
You should get them removed by an Otolaryngologist if any of then are not being removed manually by yourself..
If they are removed you can follow certain remedies to reduce the formation of stones.
You should do warm saline gargles 3 to 4 times a day.
Gargle after each meal.
Limit the intake of dairy products as they are high in calcium and will cause more events of stone formation.
Gargle using antimicrobial mouthwash as it will help in reducing infection and bad smell..
Drink plenty of water..
For swollen tonsil you can take antibiotic like
Amoxicillin and anti-inflammatory painkiller
Ibuprofen.
Hope this information helps..
Thanks and regards.
Dr.Honey Nandwani Arora.