As indicated above, it is definitely better to have few pictures (You may cover the child's eyes as such for identification privacy purposes) for the clinical identification of the same.
However, white patches at multiple places, with spreading tendencies can most likely be :
(1) Fungal Infection (Taenia): This may require a topical antifungal like Clotrimazole for local application (To apply on dry skin three times for 3 to 5 days) and to avoid near eyes/ nose and very close to mouth areas, to about it affecting the child, then neck, including the upper limbs and lower limbs. The faster spread probably means this as a possibility. (NOTE: To confirm if this is the case, kindly send a few pics). Lesions cause sometimes itchiness (which actually spreads it)...
(2) Other Possibilities, which are next Possibilities in this age group may include ---> Due to allergic reactions, presence of parchment like itchy lesions. Usually plain Calamine lotion three times a day, for a week or so, must help and oral/ syrup antihistamines for controlling the itching part, if severe....
(3) If first point is true, (1) then to find if similar lesions are present in the Mother, Husband, Or any immediate immediate contact of the child!!!!? Then we need to treat them.
(4) To improve hygiene of the child by making sure that the nails are cut, dresses changed after playing or when sweating!!! Washing hands or using alcohol based hand rubs regularly with supervision...
Next Steps
To send pics...
Health Tips
Hygiene of everyone, including child, all caretakers and those closer to the child utmost necessary...