My son used to have to hug me when throwing up.
Fortunately, it was very rare. And I could read him well
Enough to know when he was going to throw up. so I would run outside with him and try to lean back a bit with him throwing up over my shoulder. Being outside making it much easier to hose down and clean up. of course I need a shower and wash my hair but at that point it was whatever I could do just to get through it.
He’s 13 and he grew out of that and now he has to throw up he just does it him to go into the bathroom is a little bit harder. He usually freezes in place, but I’m sure your child will grow to be less afraid of it but it’s hard right now I’m sure.

My typical daughter hates being nauseous. It scares her and so I used to have her go and run her wrists under cold water in the sink and splash cold water in her face because it was kind of calming and then if she had to get sick, she would be over the sink already, or turn to the toilet, or in a bucket whatever I’d set up. but she found splashing her hands in the water was a relaxing feeling which took away some of the anxiety.
I hate throwing up as well. I think pretty much most people are somewhat panicky or afraid of it.
Also, if you could try explaining it to one of the social stories or something, so let him know exactly what’s happening because that feeling can be so alarming almost like you can’t breathe and your eyes are bulging out, so maybe he just doesn’t really quite understand what’s going on and normalizing it will ease his worry

I hate that feeling you get just before you have to throw up. It's terrifying. Thankfully, the amount of times I've gotten sick to my stomach in my life are few and far between. Hope he feels better soon!