I was taking ortho-tri cyclen mostly for its acne fighting benefits, and when the pharmacy started to get me norgestimate birth control pills instead, I started to have severe vomiting at the start of every month. I stayed on it for only 3 months. Now, I am switched to Loryna birth control pills and I just got my first pack. However, I am too afraid to take the first pill now because I heard it can cause vomiting too. Can I take half pills so I don't have the possibility of vomiting?

Can I take half pills so I don't have the possibility of vomiting?

No, you must take the whole pill for the benefits it provides. If you take half a pill, you might as well take nothing.