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No, vomiting is not normal. And, it can lead to a whole lot of problems, because it messes up your electrolyte balance. That's why it is usually suggested to get one of the gatoraid type of drinks. In infants, we use pedialyte, but if you have ever tasted it, most adults can't drink it.
You really have to stay hydrated. Try to get very small amounts to stay down. If you are not peeing at least 3 or 4 times a day, you probably need more fluids. You don't want to end up in the ER having fluids by IV.
Electrolyte imbalance can lead to things like muscle cramps, abdominal cramps, and even irregular heart beats. So, try to keep some fluids down.
Good luck.