Can I use a zinc ointment on my herpes outbreak to relive symptoms?

May or may not help. There are some non-medical "treatments" such as lysine that may lower the frequency of outbreaks, and some over-the-counter medications that can help with healing of cold sores. There are usually only a handful of research studies on each product, which doesn't mean much in the medical world. A patient can collect information and visit his doctor to see if any of the "treatments" are worth trying.