Are you sure that it's a zinc problem? I think you should go to your doctor and have a medical work-up. It could be a hormonal imbalance, a medication you're taking, a condition (such as diabetes), a scalp infection, hair treatments that damage hair, or a nutritional deficiency (not just zinc, but protein and iron).
It could be any of those things. Your doctor will want to do some blood tests and maybe take a small scalp sample. This may be an underlying medical condition that can be easily treated.