Those are probably tonsil stones! They are VERY common.
Look at the back of your throat. See the tonsils? See the holes (ducts) in the tonsils where your saliva comes out of? The stones are formed inside the tonsils and come out of these holes. Sometimes the stones get stuck in the holes and you can see the white stones poking out of the tonsils. I used to squeeze any stones out with the blunt end of a toothbrush... I had a very effective technique for doing this after I got used to it.
Tonsil stones can cause DRAGON BREATH as you might already know. With experience, I could tell when I had new stones because they would give my breath that "tonsil stone odor" Cleaning my tonsils out helps my breath immediately, and my whole mouth feels cleaner as well. I had stones since I was 13 years old. I really don't get them much anymore, but I do "clean out the tonsils" a few times a week before brushing and gargling. Instead of stones coming out now, sometimes I get a very small amount of white-ish liquid like milk coming out (sorry to be so graphic), which I believe is what turns into stones if left in the tonsils for too long - the precursor to tonsil stones if you will.
Gargling with alcohol based mouthwash helps too. If you do try to squeeze them out, use a long blunt object like the smooth end of a toothbrush, and dip it in Listerine for a few minutes before hand to kill any germs. Be gentle too - don't want to damage the tonsils!