This sounds like puss which comes from bacteria in the mouth. Ive always had them on and off on my tonsils and they come out when I cough or strain my throat. They have a horrible odor. They are usually round and lumpy and slightly green. I wouldn't be too frightened off them, just gargle with a peroxide/water mix to get rid of bacteria. They can be more re-current with allergies and post nasal drip. Best of luck!
There are a lot of different names for them. One name is tonsil stones. they are somewhat common. I get them from time to time. They do smell really bad though. I usually rinse with listerine and they will go away. I get them when I have a post nasal drip. they really are harmless.
Thankyou for your comments! :)