Im in the same boat. Sensitive skin, regular acne and cycts. Im on zinc tablets and they are helping but ive found for me coconut oil (eating it and using it as a face mask for an hr (how ever often), has helped. But what has helped the most is drinking 3Litres of water a day. Its alot, but its clearing my skin up big time. Havent had any cysts in ages (touchwood!).

I also use zinc as a supplement, but I haven't found a zinc mask. Are you going to crush a zinc pill and then dissolve it in some water?
My skin is also very sensitive and I'm allergic to BP, tretinoin and a bunch of other creams :L