Yes, oily skin is acne prone skin. This is because excessive oil or sebum can lead to comedones and active acne.
For your pimples, I suggest using topical antibiotic creams like Clindamycin (Dalacin).
For reduction in sebum production and acne over the long term, I suggest using topical retinoic acids like tretinoin (Retin A) or adapalene (Differin).
Other maintenance treatments like superficial Chemical peels (glycolic & salicylic acids) and HydraFacial also help to cleanse your skin and reduce acne.
Hope that this helps!
Warmest regards,
Dr Justin Boey