I can't comment on using essential oils (EO's) on a child, victorytea, but if I may share my own experience, I have used them on myself: InTune from DoTerra, for one. You might try a search for parent stories using the name of that product, since it was developed to address focus issues with ADHD type conditions.
My use of EO's is done in association with a whole lifestyle of healthy eating, supplementation, and other natural therapies. No matter how good an oil may be, the damaging effect of a multitude of synthetic food ingredients, possible food allergens, and toxic environments may be more than a good oil can overcome.
I know one practitioner who has seen an autistic child speak for the first time to the amazement of the parents after the child spent 10 minutes in a house with EMF (electro-magnetic field) remediation. <disclaimer>It would have to be tested before knowing a cause-effect relationship for certain,<end disclaimer> but EMF remediation is part of my lifestyle.
As YippySkippy alludes to, some oils can have strong adverse effects which could be caused by adulteration. Thinning the product or adulterating it with petrochemicals is common in the industry. I started using oils with a Lavender oil from a local store, and after getting pure French Lavender, there's no comparison between the two? well, there is, but if you compare, the first smells like brake fluid compared to the second.
I will add that pure oils can have a strong and dramatic effect, and should therefore be researched and applied carefully. The idea that they're just flowery smells they use in perfume can be misleading and potentially cause someone not to handle them with the care with which they should be.
Here's an article about how one of the early developers of modern EO's used Lavender portraying their strong potential: http://roberttisserand.com/2011/04/gattefosses-burn/
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