Check out this answer by Bill Roberts:
"A non-oily moisturizer can help.
My opinion is contrary to many on whether oils in moisturizers should absolutely be avoided or not. Many oils such as mineral oil, and oily materials such as isopropyl palmitate or myristate, indeed should be avoided. But for example one of the best anti-acne products IMO is dermaE brand Clear Skin 3 moisturizer, which contains tea tree oil, rosewood oil, and caprylic triglyceride (an MCT oil) among other ingredients. There are oils that are helpful.
Diet is also important. Increased consumption of olive and non-hydrogenated coconut oils and decreased consumption of long-chain saturated fats (which means pretty much any saturated fat except coconut oil) seems to help a lot.
Many say that sugar worsens acne. I don’t see any evidence that glucose in pre and post workout drinks promotes acne, nor does say having an apple for a snack promote acne, but sugar consumption throughout the day indeed probably does.
Lastly, while alone it’s not the fix, and some say that long-term it worsens the problem (I don’t think that’s at all remotely the case if other needed changes are put into place) sun exposure seems to help. Not so much as to get any sunburn, but an amount reasonable for the individual case."