Oily skin need not be the only reason for acne. The sebaceous glands could be still blocked leading to infection of the area and formation of acne. It is generally influenced by androgens and that is why more during puberty time.
Homeopathic Medicine has excellent remedies like Phoshporus, Natrum mur, Sarsaparilla, Hepar sulph, Merc sol etc. to get rid of the Acne
and see that they do not recur whether it is dry or oily skin.