I used to have emetophobia as a teenager, it was all I would think about at times and I went out of my way to avoid catching bugs. I would be terrified if I saw human or animal sick in the street, or if I was near someone who mentioned they'd been sick.
I still practice good hygiene (being aware of touching public surfaces, washing my hands afterwards etc) and have not had a stomach bug since I was 10 or 11.
I will probably get dragged for the rest of what I'm going to say but it's the truth. I was cured or my vomiting phobia in my late teens by binge drinking. I was sick for the first time since my stomach bug, and it just wasn't that bad. I'm not recommending binge drinking, just using this experience to point out that the feeling of vomiting is really not that bad. Your mind builds it up, and without that anxiety, it's just an unpleasant physical feeling that lasts about 10 seconds.
The second thing is that you can stop a stomach virus in its tracks by drinking diluted iodine, which is strongly anti-viral and anti-bacterial. You add no more than a few drops of Lugol's iodine to water (how much exactly depends on the concentration of the Lugol's, you can get different %). This is safe, providing you don't have a thyroid condition or a selenium deficiency - do your research if you want to try this.
I now have endometriosis, and sometimes this makes me be sick, so I'm very glad my phobia resolved itself. I still feel a bit of panic when I feel sick because that pathway is in my mind, but not as strongly, and only when I'm approaching being sick, and never otherwise.
Finally, again this is not politically correct but it is true: I went vegan when I was 15, and my sick no longer tastes or smells of sick at all, it's just like pure regurgitated food. This makes the experience of being sick less unpleasant.
You can manage this: sick bugs typically only last 24-48 hours, that's less than most colds. You'll get through this, have some bland snacks on hand like plain rice cakes, and a bucket nearby, and enjoy an excuse for a whole day of time-wasting on your phone or watching TV.