'I fainted' is correct The other should read: 'I lost consciousness'. They are very similar in meaning. 'I fainted' is better if you lost consciousness for a short time (less than 10 seconds), and 'I lost consciousness' if it was for a longer time. But neither would wrong. A colloquial way to say this in English would be: 'I fainted. I went out like a light' 'I lost consciousness. I was out for over a minute.'

I lost consciousness. Remove the my. And they basically mean the same thing. They both are strong, however the way fainted sounds (especially how you say it) it can sound weaker. But they both mean the same thing and are fine to use.