Change Your Pillowcases
Now, we're not suggesting you're lazy at laundry or anything, but more often than not, the cause of weird breakouts on one particular side of the face can be put down to your pillowcase and the way you sleep. So it's time for a double-pronged attack. Firstly, buy extra pillowcases (cotton, not synthetic), and ensure you have a couple of clean ones spare at all time. Change them as often as you can, and see if it makes a difference.
Secondly, try to sleep on your back if you can, keeping your face off your pillow. It might not work — chances are you'll start there but wake up in the morning face down in a pool of your own drool like usual — but it's worth a try, right?