First, I think it's important to start by saying the fear of throwing up is call emetophobia, and it's a disorder that impacts a lot of people. I want to start with that because it's not something you can just "tough out", it requires dedicated effort to overcome. With that said, the only clinically proven treatment for emetophobia is therapy, CBT and ERP to be specific.
These answers come from people facing the same fears, using exposure therapy that has helped thousands take their next brave step. See their wins and add your own.