I agree with others that it could either be some sort of adaptation, a detox, or an allergy/sensitivity.
With that said, how often do you drink coffee? I've had skin issues after drinking coffee in the past. Do you eat dark chocolate at all? If so, how often? I've heard of many people having bad skin issues when consuming cacao. It could very well be the water in your area, and it could also be your body adjusting to the lack of dairy. Try to drink the cleanest water you can and continue to be dairy-free and monitor your progress.
I had a vicious form of Seborrheic Dermatitis; it sounds like you have the same.
Seb derm - Treating seborrheic dermatitis with raw honey and virgin coconut oil.
It saved my life (along with going Primal, which accelerated my recovery).
If you have that kind of reaction to coconut oil, even localized, I wouldn't use it at all. Do you use it in cooking?
I can't stand the smell, so I don't use it myself. I wonder if that's just me being picky or it indicates a nut sensitivity.
Journal on depression/anxiety
Curing IBS-C with Vitamin C and magnesium citrate.