When using essential oils, great care should be given for those with asthma, COPD, and other breathing disorders. This information can also apply to those who are sensitive fragrances or chemicals.
The essential oils that may be useful for one person, may trigger an adverse reaction in another. Allergies may also worsen symptoms. Until you know how you react to specific essential oils, it is best to limit direct inhalation and use a low dilution when applying topically.
Specific essential oils which are more prone to be problematic are: Eucalyptus, Oregano, Peppermint, Rosemary, and Wintergreen – which, incidentally, are not recommended for children (more info here: Using Essential Oils Safely with Children)
Keep in mind any essential oil can trigger an adverse reaction, and the adverse reaction may not reveal itself right away.
If you wish to use potentially problematic essential oils around someone with breathing issues, using a personal inhaler is a discreet way which limits only yourself to the essential oils you are inhaling.
If asthma, COPD, or other breathing disorder is serious it might be best to avoid essential oils of any kind until the affected person can have a full consultation with a qualified aromatherapist who can review health history, medications, other necessary factors and also will consult with respective physicians of the person in question.