You might want to try adding foods higher in zinc. I think pumpkin seeds are high in zinc and are often recommended for men for their prostate....

There are other foods also. I'd google foods high in zinc. You may not be able to tolerate the supplement kind, OR something else contained in the supplement.

I take a multi vitamin/mineral powder, which I mix in water like an orange drink (though it contains no sugar) and that contains zinc already in there. perhaps you could find a similar mix? The combination of everything may help you keep it down too.