Does vomiting mean i'm on ketosis?

It's "in ketosis", and a low carb diet should NOT make you vomit. Even in the first few days of induction nausea is not normal. You are probably not drinking enough water and are simply dehydrated. Low carbers need to drink a LOT of water, especially in the early days of the diet while your system is flushing out all the toxins. Hang in there, it will get easier and you will feel better than you ever felt before.