Use Simple deodorant roll on. It's unperfumed and good for sensitive skins. My mum uses it and she loves the fact it doesn't sting or leave white marks. Failing that, see your doctor and he should be able to offer advice.

'Toms of Main' unperfumed deodorant is obtainable from JS and some Health Shops. Made from natural herbal ingredients it therefore contains no aluminium (unlike a lot of other deodorants/antiperspirants).