hi It looks like you child has developed pityriasis alba. Pityriasis alba is a common skin condition mostly occurring in children and usually seen as dry, fine-scaled, pale patches on the face. It is self-limiting and usually only requires use of moisturizercreams.The condition is so named for the fine scaly appearance initially present (pityriasis) and the pallor of the patches that develop. The condition is most often seen in children between the ages of 3 and 16 years and is more common in males than females.It may occur more frequently in lighter-skinned patients, but is more apparent in those with darker complexions. No treatment is required and the patches in time will settle. The redness, scale and itch if present may be managed with simple emollients and sometimes hydrocortisone, a weak steroid, is also used .But it takes some time to improve.. As Far as the hair fall is concerned, i think since the child is very young, you can just try to improve the diet of the child. Add biotin rich foods like raw egg yolk, liver, cow s milk dairy products, leafy green vegetables,cabbage, spinach , carrots, onions, broccoli, and cauliflower. Fruits such as berries and tomatoes and peanuts also are rich in biotin.. Hope it helps Dr Geetika Paul