It would be difficult to assess without having a look at the lesions. However, it seems from your description that the lesions might be some kind of allergic eruptions, milia, heat rash, skin infections / contact dermatitis.
Hives are usually allergic caused by food and insect stings also besides medication or cosmetics. Sometimes they may also be due to infections, heat, cold or stress (emotional / physical). Many a times no specific cause for them is ever found. They usually go away on their own after sometime, but in a few cases persist and medicine might be needed. The most commonly used oral treatments are antihistaminics (such as cetirizine, loratidine, benadryl available over the counter).
Milia, also known as milk spots are pearl-like whiteheads (may look like small grains of sand). They occur across the upper cheeks, under eyes, nose or chin and sometimes on the genitalia. They are benign, keratin-filled cysts seen in people of all ages. Milia are formed directly from sloughed-off skin and usually found on the faces of infants and adults.
They can result from use of harsh cosmetics or heat stress from sunlight or hot showers.
You should consult a doctor (or a cosmetologist) for diagnosis and treatment.