Well, the bad smelling, small yellowish chunks that comes into your mouth or you feel at the back of your throat are called Tonsilloliths or Tonsil Stones.
Tonsilloliths are stinky globs of calcified mucus, dead cells, debris and bacteria that form in the tonsil crypts (small pockets or divots that is in everybody's tonsils). They are composed of calcium, but may contain other minerals such as phosphorus and magnesium, as well as ammonia and carbonate.
Tonsilloliths are one of the causes of Halitosis (bad breath). They usually apear as tiny little chunks in the shape of cauliflower and smell very bad. True tonsillar stones are rare, small areas of calcification or concretions are relatively common.
Tonsil stones sizes can range from a small peppercorn to a larger size causing throat discomfort and in some cases uncomfortable side effects including sore throat, ear pain or tonsillitis. It has been recorded weighing from 0.3g to 42g.
They are common in both adult and children. However, they often occur mostly in people who suffer from chronic inflammation of their tonsils or recurrent tonsillitis. Studies have shown that people who have had their tonsils removed, under most circumstances, almost never experience tonsil stones (well because they don't have tonsils).
Often no treatment is needed, as few stones
produce symptoms. Some people are able to remove tonsil stones using the tip of the tongue. Oral irrigators are also simple yet effective and will thoroughly clean the tonsil crypts.
More simply still, gargling with warm, salty water may help alleviate the discomfort of tonsillitis, which often accompanies tonsil stones. Vigorous gargling each morning can also keep the tonsil crypts clear of all but the most persistent tonsilloliths.
Also Curretages, Laser and Tonsillectomy (removal of tonsils) can also be done. But, tonsillectomy is not the best option because with tonsillectomy, you stand a chance of developing recurrent mouth infection as the Tonsils are part of the the immune system and function like nets and trap incoming bacterias and viruses passing through your throat.