What you wrote suggest you have a congested liver. I threw up in one of my first flushes and it was when my liver was badly congested.
Drinking water after the oil tends to cause the vomiting. In my experience we should take the oil plus juice and nothing else for at least 8 to 10 hours sometimes even longer and only then we should go for the water to help hydrate the body.
Another important element: I know may people take several doses of Epsom Salt I take only one two hours before the Oil+Juice and that seems to be enough
As Hanna said, even when we throw up the flush is likely to work, but of course not 100%.
Donīt give up! You took the fisrt brave big step. the first flush is always the most fearful, but hopefully your results will be good and you should think of a next one to decongest your liver.