One more day that I'm alive and well

It has been a stressful week in babysitting. Twice in the past 5 days two different kids choked and one consequently vomited twice. The first was the 15 month old I've babysat only a handful of times. She has a habit of not swallowing all of her food and just letting it loll about in her mouth an hour after lunch has ended. Her mother knows it's a problem, but unless she's putting her to bed doesn't worry about it. I was sitting on the family room floor with her when she started her "crying because I'm there and NOT mommy" which is a fun cycle that continues endlessly the entire 3-4 hours I am there. This time, however, she started with a gasp followed by awful "I can't breathe" sounds. Since she's tiny, only about 16 pounds because she was born about 3 months too early, I whisked her up, slung her over my arm and gently (of course) whacked her on the back. She continued her usual screaming after that. I only told her mother that she started choking a little bit and that I had to hit her on the back, which is why she is crying more than usual. I figured there was no point in worrying her mother any more than necessary. All's well that ends well.
Yesterday I was watching the two boys aged 27 months and 9 months. The 9 month old had been happily playing on the floor by himself for nearly an hour when I looked over and saw something white in his mouth, most likely one of the dinosaur stickers his brother had been sticking on and peeling off everything. Just as I started to walk over to look closer, he gagged and puked. Twice. He started screaming when I pulled his shirt off and tried to wipe the snot from his nose. He is also getting over a bad cold, so it's possible that he choked on his own phlegm, which is what I told his parents. He seemed fine after a sink bath and some pedialyte.
Here's the thing. Vomiting of any kind freaks me out. I know, nobody enjoys it, but I think there are probably people who don't mind it as much as I do. I've only thrown up a handful of times in my life, and before the last two times it had been 12 years since I'd been sick like that. I start to imagine being horribly sick which makes me feel so out of control. Maybe that's the issue for me-the lack of control over vomiting. With a cold or a headache you can still go about your day, but not when there's puking involved.
Last night, as I was trying to fall alseep and hoping I wouldn't catch the baby's choking-vomiting bug, the only thing worse that I could envision happening to me that night was death. Luckily I evaded both.