A few months ago I broke out very badly, badly enough to contact my doctor to ask for advice. He recommended me use a La Roche-Posay face wash, which is perfect for oily skin as it removes more of the oils than other brands. I did use it but unfortunately I have combination skin (some oily parts, some dry) and it wasn't ideal for me as it caused me to have overdry skin, but it has very good reviews so it may work better for you. The doctor also prescribed me another cream with some medication in it, so if you are overly worried I'd contact your doctor to see if they could prescribe you something like that.
I'm quite big on skincare overall and my current combination I use is Olay products - a face wash 2x a day, day lotion and night cream. They have different types of each product specifically for oily or dry skin etc, so I use a dry skin face wash and a sensitive skin lotion, so far my skin has stayed relatively clear. But I'd first try La Roche-Posay in your case, and maybe a cream at least once a day that is designed for acne-prone or sensitive skin to not overdry.