actually, there *are* a few essential oils that would possibly have the ability to penetrate through the blood-brain barrier.... the one ones containing sesquiterpenes — but most of those particular eo's are not considered anti-anxiety or stress-relieving . Many unadulterated essential oils have the ability to penetrate cellular membranes, depending on the oil.
I recently had a bout of severe bronchitis which turned into pneumonia... still have the remnants of it. Because I can't take antibiotics, I used essential oils diffused into the air... particularly frankincense, niaouli, and lemon. Probably didn't work as fast as antibiotics might have, but it did the trick.
I've been a certified aromatherapist for over 20 years, amongst all the other healthcare technologies in which I'm certified. Not all of us subscribe to the nonsense that some in the essential oil business have been purporting. But essential oils definitely have healing properties.
(By the way, I did PhD level research on the chemical constituents of essential oils. It bothers me that so many people use them indiscriminately....gives a bad rap to those of us who actually know what we're doing. I would consider the proper use of essential oils far and above the use of homeopathic drugs that are (in my opinion) basically worthless.)