This is what the NHS has to say about zinc.
http://www.nhs.uk/news/2012/05may/Pages/Zinc-shortens-common-cold.aspx
Conclusion
For many years, it has been suggested that zinc supplements could relieve the symptoms of the common cold, but there was little clarity until a 2011 evidence review. This recent review suggested a modest reduction in the length of symptoms, although the results were not entirely conclusive. In a bid to help clarify the matter, researchers have conducted another review of evidence on this issue.
It suggests that zinc may help shorten the common cold. However, as with the previous reviews, the results are undermined by the high variability between trials in terms of their methods, study population and treatment aspects (such as zinc dosage and when zinc was first taken). In addition, while zinc may help shorten a cold, it also seems to have side effects such as nausea and an unpleasant taste. As the authors point out, large-scale randomised trials would be needed to assess whether the potential benefits of zinc outweigh the side effects, as well as what dose might be optimal. However, colds are a minor illness for most people, so whether such a trial is warranted is debatable.
From a nutritional perspective, the recommended daily intake of zinc is 5.5–9.5mg a day for men, and 4–7mg a day for women. It should be possible to obtain this amount through a normal balanced diet. If supplementary zinc is taken, the Food Standards Agency and Department of Health recommend that no more than 25mg a day is taken, as too much may cause anaemia and weakening of the bones.