Is there a specific scent for each illness?

I wouldn't say that one type of oil will cure or alleviate one particular illness. It's usually a mixture of oils and the results vary with different people. For example, I've used essential oils for nausea and vomiting and mint, ginger, lemon, clary sage, juniper, eucalyptus, rosemary, peppermint and green apple essential oils are some of the few you can try. I've personally tried peppermint, lemon and ginger. The one I thought gave instant relief is ginger.