as you know since i cannot see it first-hand i cannot offer you a definitive answer. i do not know anything about you or your medical history so i suggest that you show this spot to a medical professional. it has been there six months now so this would be advisable. as a guess you may want to look up "tonsilliths". these are accumulations of food and other debris that can be trapped in tonsillar tissue.
i have a pea size white spot on the back of my throat. it has been there for at least 6 months! right of my tonsil