This is just my opinion, so take with a grain of salt...

I have no problem with the word vomit. I have no problem with characters vomiting in a story. The manuscript I'm currently working on has the main character vomiting quite a few times due to chronic illness. If it's needed, use it.

It does gross me out a bit when authors go to great pains to describe the actual vomit in fine detail as if it's a menu item at a five-star restaurant. Particularly when the vomiting happens multiple times in the book, and the describing goes on and on, detailing the chunks, how they feel coming up, the exact yellowness of the bile, I start to turn green and wonder what is with this author and vomit? One of the books I read recently where this happened was a romance!

For me, it's like characters using the bathroom. If there's a good reason to show it story-wise, do so. If there's a good reason to describe it in detail, do so. And know there will be some people who find certain body functions yucky.