Which word can I use to describe the sound somebody makes while vomiting? Is burp the right word for it?
I would say that the sound made by vomiting is retching. I've also seen retching noises or the sound of retching used in print to specify the sound instead of the action.
Mirriam-Webster online give this definition:
transitive verb : vomit 1 intransitive verb : to make an effort to vomit; also : vomit
I was having a great time until I heard the sound of retching and saw that my neighbor had just vomited on my new rug. I'm sending him the cleaning bill.
Here are some 147 terms for ‘to vomit’. Interestingly, it says 57 of these, i.e. approximately 38%, come from or are primarily used in Australia.
Here are dozens more, but focussing on the sound itself, I think the most onomatopoeic one is...
Another high-scorer on the "onomatopoeic scale" is hurling [over the toilet bowl].
Puke, barf and ralph are used in certain regions. They all mean "vomit" (the verb, not the sound) but are so onomatopoeic that to my mind they apply to the sound as well.