I have a phobia of being sick, but others vomiting isn't an issue. I do panic, but, selfishly, it's in case it means I'm going to be sick. I have a germ phobia too, partly for fear of an infection that will make me sick (hand washing, avoiding situations, avoiding people are/who have been ill, etc), partly health anxiety. DS1 is the next stage up from me, he's hysterical if he even hears someone vomiting, cries if he feels even slightly queasy, it's pure panic and he has no control over it. He's been like this since he was five and his friend projectile vomited at a sleepover.
I have lots of phobias, including holes (and lumps, bumps and things out of place) which I've always had. It's a real thing. I couldn't look at a sponge when I was small. I feel ill and I panic in the same way as I do when I see a spider. I have anxiety shit going on too. I can't remember not feeling anxious to some degree. As a child I was prescribed Gaviscon tablets for 'a nervous tummy' which had a good placebo effect. Beta Blockers do a similar thing now.
I'm well over 40, and this has been going on since I was 7-8, so it's not a new thing, I think we're just not scared to talk about it now. Some of my best friends don't know how bad I am, and I would never sit in a pub/cafe and have a conversation about these things, but on an anonymous forum online I'm happy to discuss them.