what you are experiencing are called "tonsil stones". I have actully had them for a super long time. They do not give me foul smelling breath or anything, the only thing is that they sometimes dislodge from the tonsil. They are putrid smelling and can be whiteor yellowish soft balls. I take a flash light or lighted mirror and open my mouth and take a small dentist instrument and gently pull them out of my tonsil. It sounds soooo nasty, but I would much rather pull them out then have them hang out in there. My Dr. said that you can use a Q-tip, but that is too blunt and does not work. They are just pieces of food that get stuck...you can gargle, but this usually does not help them loosen. My one friend said that he just coughs them up when he feels one against his tongue...they are not plesant, but they are harmless.
I hope that this helps
I have the same problem and it makes me have bad breath. I have heard the explanation that your throat sometimes has little pockets where food gets caught and then sits there and creates those little white balls. I haven't heard how to make them go away though.