Latex sensitisation is a serious problem. It is estimated that up to 3.6 million people in Britain are already sensitised, including 17% of nurses. It costs employers, like the NHS, millions of pounds in days lost through sickness. Do try and speak to whoever is responsible for health and safety issuesin your organisation.
Once you have told your employer that you have a health issue it is their responsibility to look after your welfare. They also have a duty to keep information about your health confidential unless you give them permission to disclose it, so not everyone has to be told of your sensitivity to latex, if that's not what you want. Your employer simply has to take steps to make sure you stay safe, like making sure no balloons are used.
