Meaning of 喉まで出かかる

Question

マクゴナガル先生は口を開きかけたが、思いなおして、喉まで出かかった言葉をのみ込んだ。
Professor McGonagall began to open her mouth, but reconsidered and swallowed her words.

My translation does not include 喉まで出かかった. Is this a set phrase? Would the sentence remain natural if 喉まで出かかった was omitted?

I see a translation of 出かかる of "to be on the tip of one's tongue" in Jisho. This seems related but it's not clear to me how it would be used.

I think a literal translation of 喉まで出かかった言葉 would be "words which emerged as far as the throat", suggesting that the concept is that words start in the stomach, progress through the throat, and finally emerge from the mouth. Is this correct?

I think some example sentences of how 出かかる (or the whole phrase 喉まで出かかった) is used in real-life may be helpful.

Answer 1

喉まで出かかった is a set phrase that means "almost said". It suggests that the words came from somewhere else (I don't know if it's the brain or the stomach) but were blocked before being vocalized by the throat.

Would the sentence remain natural if 喉まで出かかった was omitted?

The sentence still makes sense without it, but of course some meaning will be lost.