Hi, welcome to the forum, some causes for itchy bumps are folliculitis, fungal infection, acne or allergy.
Acne usually develops due to increased sebum production. You should wash your face using a mild skin cleanser and warm (not hot) water. Skin cleansers should be slightly acidic and intended for the face (rather than the body).
It needs to be differentiated from infectious folliculitis (secondary to infection) as skin is enriched with hair follicles. It may be due to bacteria like staphylococcus, streptococcus etc. Other possibilities are fungal infection (tenia barbae) or irritant dermatitis etc.
Picking or squeezing lesions should be avoided as this may worsen lesions and cause inflammation and scarring as your hands are prime source of infection. Moisturizers and Sun protection will help protect the skin. Try to take more water.
Topical retinoids halts the progression of acne and comedones, Benzoyl peroxide is a dissolves comedones and topical antibiotics or anti fungal (if skin infection present) are very helpful and should be taken after consultation from a dermatologist. Take care and regards
It might be an allergy to makeup or even your face soap try a different face soap and stop wearing makeup for a while. As for what to put on it try using a clean make up brush and brush on corn starch like the kind you find in the kitchen.
If that doesn't help I would ask your mom to take you to an allergist the doctor can test you to find out for sure and can prescribe a cream to put on it.