Are you 100% sure that you're removing ALLLLL of your make up? I had a similar problem and it was because i was using a lotion that wasn't removing what it was supposed to. So i went to estee lauder, i purchased a cleanser ("PERFECTLY CLEAN" (normal/combination skin), the toner, and the facial scrub. It might have cost a little but i think it is worth it, and i've noticed a big improvement. The cleanser does a fantastic job of removing all my make up, the toner freshens and neutralizes the skin, and the scrub i use once a week to remove gunk from the pores and get rid of flakiness/dead skin cells. A little goes a long way with the cleanser.
I had previously been using clinique, and i noticed that no matter how much i tried using their clarifying lotion and the facial mousse, the make up would still be there...the morning after. So i switched to EL, and i know i've made a good choice
Good luck~
P.S try drinking LOTS of water..it flushes out all the bad toxins in your body and is great for the skin
AHA and BHA work well for me for blackheads, but for whiteheads, I find benzoyl peroxide to work best!! I really like Paula's Choice 8% AHA and 1% BHA liquid. For benzoyl peroxide products, I like Paula's Choice Blemish Fighting Solution and Proactiv Repairing Lotion. Both of these are 2.5% benzoyl peroxide. HTHS!!
I have worked for clinique for 3 yrs. The pore minimizer thermal active refiner, would more than likely do the trick. It has really helped me out. I had the same problem. You only use it twice a week or so and exfoilate the other five days a week.