Sea level is not the minimum oxygen levels tolerable by your body. Why, just a month or two ago I climbed to 14,000ft. Made me dizzy and nauseous , but the partial pressure was somewhere around 80mmHg.
Humans can function to varying degrees at lower partial pressures of O2 than you experience at sea level (obviously, since people live at altitudes of up to 12K ft).
If you have not adapted to high altitude, you will experience cognitive decline at altitudes much higher than 10K ft, although they can be imperceptible. You can also go up to 30K ft, lose consciousness, but experience no long term harm as long as it's not for extended periods of time.
There have been glider pilots who have been caught in massive up drafts, climbed to 30K ft or higher, lost consciousness, then regained consciousness when they descended and safely landed their planes.
http://www.smh.com.au/news/national/dead-luck-ewas-flight-of...
Regardless (and I feel like such a broken record saying this), meaning in language is determined by consensus, not dictum, and at least for me (a 21 year old who grew up in the United States), "nauseous" can have no meaning but "sickened". "Nauseating" is what I would use for your meaning.