You clearly didn't just 'try' Vodka if you were vomiting. You drank to excess.
That sounds like a lot of vodka, especially for a first-time drinker! Depending on the size of the cup, that was likely at least 5 drinks, and likely more (1 drink of spirits is usually less than you think, and almost always less than what you see poured on TV).
Given that it is also easier to drink liquor faster than something like beer, you likely had quite a bit of alcohol in a pretty short time. I'd be sick, too.
The kind of vodka that someone having their first drink does not go down quicker than beer unless you're already drunk.
Measures poured at someone's home tend to be more than 35ml.