What oils are used for inhalation?
If the cough is dry, it is recommended to use essential oils of eucalyptus, peppermint, oregano (oregano), tea and clove, basil, frankincense. When the cough becomes wet, oils that act as expectorants will help: Atlas cedar, Scotch pine, medicinal rosemary, peppermint, thyme (creeping thyme), noble laurel, tea tree and the same eucalyptus globular.
Essential oils for nasal inhalation - fir, cedar, cypress, eucalyptus, mint - are not only strong antiseptics, but also work as decongestants, that is, they relieve swelling of the mucous membranes of the nasal cavity. For more details, see - Treatment of the common cold with inhalations .
Eucalyptus oil for inhalation is valued for its antiviral and antimicrobial properties and anti-inflammatory activity, which are provided by a cyclic ester - monoterpene 1,8-cineol or eucalyptol (which accounts for 73% of all chemical components of this oil). 
Inhalations with this oil relieve and soothe cough in any respiratory diseases. And many experts believe that this is the best oil for inhalation, since not only its ability to relieve bronchospasm and reduce the intensity of inflammatory processes (by blocking pro-inflammatory cytokines) has been proven, but also to destroy the accumulated tracheobronchial secret and cleanse the respiratory system.
The basis of peppermint oil is terpenoids menthol and menthone (in total - 65-87% of the composition); there is also 1,8-cineol (5-12%). Menthol, when inhaled, creates a cooling sensation that can soothe a scratchy and sore throat and relieve nasal congestion. Peppermint oil for inhalation helps in the fight against viral infection, improves the mucociliary clearance of the respiratory tract and relaxes the muscles of the windpipe, making it easier to breathe when coughing. Menthone (terpene ketone) neutralizes the action of free radicals, that is, it is an antioxidant. 
Tea tree oil for inhalation with a sore throat or cough is not much inferior to eucalyptus oil (although it contains 4.5 times less 1,8-cineole), and in terms of antiviral and antibacterial activity it far exceeds mint oil, since it contains almost 30 % terpinen-4-ol. 
In acute bronchitis with an unproductive cough, fir oil for inhalation weakens its attacks, and with a productive cough, it facilitates sputum discharge and relieves bronchial spasms. 
The essential oil of Atlas cedar, used for inhalation during coughing, helps to thin sputum, and with a runny nose - a thick nasal secret. A similar effect, due to the high content of 1,8-cineol (almost 45% of the total composition), has rosemary essential oil.
Like the plants themselves, essential oils of oregano and thyme contain powerful antibacterial components - the phenol-derived terpenes carvacrol and thymol. Many herbal cough remedies contain extracts of these medicinal herbs.
Sage essential oil for inhalation, containing about 15% eucalyptol, as well as thujone (22-60%), alpha-pinene, borneol and camphor, is an effective expectorant. However, the predominance of the monoterpene ketone thujone, which negatively affects the central nervous system, limits the use of this essential oil, as it can cause convulsions. Therefore, this oil can only be used for so-called cold inhalations, when a few drops of oil are dropped onto a swab and its vapors are inhaled. 
A mixture of essential oils of the Olbas trademark and its synonym (produced in the Russian Federation) - Dyshi oil for inhalation - contains oils of peppermint, eucalyptus, juniper, clove, cajeput (a type of tea tree) and gualteria, as well as L-menthol. The oil is intended for the prevention of respiratory infections: it is used by cold inhalation. The instructions for Dyshi oil indicate that it can be used by children from 12 months of age, however, clove oil is contraindicated for children under two years old, and peppermint oil and L-menthol - up to five years.
Some sources recommend the use of sea buckthorn oil for inhalation for sore throats, but this oil is not an essential oil and does not contain volatile volatile compounds (it contains omega fatty acids and carotenoids). It is more rational to lubricate inflamed tonsils with this oil. Read more - Sea buckthorn oil for angina . 
Peach oil for inhalation is no less problematic to use - for the same reasons, but it can be used to lubricate the nasal passages with dry nasal mucosa or to soften crusts in the nose with a runny nose in children. 
Oils for inhalation during pregnancy
Essential oils for inhalation such as juniper, clove and cajuput are contraindicated for pregnant women. In addition, oils of peppermint, oregano, thyme, sage, fir, cedar, tea tree (due to the hormonal effect and neurotonic effects), cypress (in the first half of gestation) are not used during the period of bearing a child.
More information in the material - Inhalations during pregnancy .
The list of essential oils that are contraindicated for lactating women is a little less, but it should be remembered that sage essential oil reduces lactation.
Oils for inhalation for children
The ability to use oils for inhalation for children depends on their age, since the lobes of the lungs continue to grow until the age of three, and the bronchopulmonary system is fully formed only by the age of seven.
Essential oils are extremely potent substances and their use in children requires special care. For safety reasons, it is contraindicated to use eucalyptus oil for inhalation - until the age of one year (in some recommendations, even up to three years); up to two years - cloves; up to three years - fir; up to five years - thyme oil; up to five years - mint and rosemary oil; tea tree oil - up to 10 years, and oregano and cedar oils - up to 12 years of age.