Hi. Based on your description, those white patches might be "tonsilloliths". They are just the ground up food particles, mixed with dead cells and bacteria that get deposited over the furrows of the tonsils.
What's of concern regarding them is that they might cause halitosis (bad smelling breath) and could be a source of recurrent throat infections.
Your child's infrequent brushing may very well have contributed to those white spots.
Next Steps
Kindly get an ENT consultation to confirm the diagnosis.
Health Tips
Good oral hygiene - brushing twice a day, Gargling after every meal and before bed; these will remove the tonsilloliths most of the times.
Good day.