Can you tell me can I randomly become allergic to makeup?

Allergic dermatitis. Random might as well be the term for it; we tend to use the term idiopathic. Though we understand what process is involved, we don't know why certain people develop allergy to products applied on the skin. Cosmetic allergy is very common, and occurs sometimes after years of use. Patch testing can help identify the specific ingredient causing the allergy. Seek out a board certified allergist.