I HATE ME when I'm like that. I feel all nauseous and weepy now. But at least spiders people understand. Nobody understands emet. If I did, I'd probably have advance warnning and could run away somewhere.
Adults do occasionally throw up in public and the world goes on.
I would not die. I would not be mortally wounded. I would not be terminally embarrased. It might be icky and upsetting bit it would not be fatal. Even engine mechanics can be scared of spiders.