Zits, or pimples, are medically known as closed comedones. The disease by which we get these is known as acne
vulgaris. Acne vulgaris is a common medical condition, yet unfortunately there is still we do not understand about the process by which the pimples develop. Regardless, we do have very good treatments for it. I would recommend that you discuss this with a dermatologist
(a skin specialist) who can help both diagnose the exact cause and subsequently treat.
Comedones are when the pores of the skin become clogged. These pores are throughout the skin and are opening for sebum -- the oily substance by which the skin lubricates the small hair on our body. When these pores become clogged with oil they can either remain open and the oily substance becomes oxidized -- this is known as a blackhead. If it "closes" it traps bacteria and inflammation / infection occurs -- this is a closed comedone or pimple. Why some people increase sebum production at different times in life (like with hormonal changes during puberty) are not completely understood. There are some conditions (abnormal steroid production) that can exacerbate the condition. Medications can also worsen pimples.
A dermatologist can help identify the cause and treat these. There are creams, soaps, pills and other laser treatments available. Good luck!