I've had internal problems causing acne for a while. My nails were brittle and splitting and I had plenty of white spots, so I figured zinc had to factor in somewhere. As far as the acne went, all my breakouts have been on my chin, generally starting cystic and painful, and have been there consistent for a few years now. When one pimple cleared up, yet another would show up painful and aching. It didn't matter how much I washed my face or what I used to do so. Clearly hormonal.
I started taking 100 mg of zinc gluconate (two 50 mg pills). About a week after starting that I also started nightly benzoyl peroxide applications to my chin. Together they're clearing it up entirely - the zinc fixing the internal problems, the peroxide killing whatever was on the surface and helping clear up blackheads in the process, a nice bonus. Very relieved this worked. i will likely scale my dose WAY back once the majority of my acne clears up, as I doubt whatever zinc deficiency I have requires the full 100 mg, which I took mostly out of desperation. 50 mg might have worked just as well, I couldn't say, I didn't try it. I'd recommend starting at 50 mg (which I didn't do) and if that doesn't help, up your dose at that point.