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Acne and Oily skin, go hand in hand.
While it is important to use a cleanser that would clean excessive oil from face, it should not leave behind a feeling of dryness after washing.
Over drying face washes are in fact counterproductive because sebaceous glands which are already working overtime would try to compensate dryness and therefore cause rebound oiliness.
I would suggest a gentle cleanser for face wash e.g cetaphil cleansing lotion, twice daily.
Besides, you may use topical
benzoyl peroxide or
clindamycin gel during day time as a spot treatment for active acne.
At night I would suggest a topical retinoid e.g adapalene gel, over the whole acne affected area.
I suggest you to visit a
dermatologist. Your dermatologist will assess the severity of your acne and advice accordingly.
Your dermatologist might also start you on
Oral antibiotics if your acne is Inflammatory i.e red, pustular or painful.
You may also opt for a few sessions of chemical peeling from your treating dermatologist.
Salicylic acid chemical peeling is quite good for acne and oily skin conditions.
Regards