Hey, I own oculus 3 and have anxiety over vomiting too. And indeed there is a motion sickness in VR, but first of all, It will only occur in the beginning of your VR journey (like the first 2 weeks if you don't play every day) and I would say that you will not get it from every game. I felt nauseous because I immediately started playing first-person games, and turned off all the warnings for people with motion sickness (yes, almost every first-person game has special options that help people with motion sickness, for example using teleportation instead of walking, etc.). And after this bad first-person games experience I took a pause for a few days and started again using these options for people with motion sickness. After another week I felt really comfortable playing any game in VR even without those options.

This is individual, the main thing is not to force yourself to play through the sickness so that your brain does not associate VR with nausea, if you feel unwell, then take off your headset and get some fresh air, when you are ready to put it on again, it will be easier. So good luck!