you might be allergic to something in your cleanser. i'm allergic to benzoyl peroxide which is a main ingredient in alot of acne clearing products. but i finally realized that to get rid of your acne, i needed to wash my face multiple times a day. after washing my face, i needed to put moisturizer on it in order to not let it dry up. if it dries up, it might get irritated.
after using your cleanser, try putting some moisturizer on it (i use neutrogena) because your skin lacks the natural oils due to the washings. you need to put moisture back on your face or else your skin will look for excess oils which can cause breakouts and acne.
if this doesn't work, then you should switch your cleanser or consult a dermatologist. goodluck.