Those "white balls" are actually tonsilloliths and are tiny particles of decaying food. They cause bad breath, sore throat, and the feeling that something is "caught" in your throat. Left untreated they can lead to tonsillitis. You should seek medical attention for this.
Those are puss balls, you get them from strep throat, and sometimes just a sore throat. It will be fine if that's the only problem. If you start to feel cold like and feverish, you need meds from the doctor. they will most likely prescribe Zithromax.