Rev 12:15 explicitly says what came from the mouth of the serpent. It was water, ὕδωρ (hydōr). Further, this is described as a "river of water" which was a significant torrent because the verb translated "spewed" is the verb βάλλω (balló) meaning to thrust, cast, throw, etc.
I can find no allusion to vomit anywhere here. However, we later find an interesting statement that assists in the interpretation of some passages, Rev 17:15,
The waters you saw, where the prostitute sits, are peoples,
multitudes, nations and languages.
If we use a consistent hermeneutic, this might be applied in Rev 12:15 as well, meaning that the serpent somehow marshals large numbers of people against the woman (after she had given birth to the male child who was caught up to heaven). Thus, the dragon tries to sweep away the woman not the male child.
Indeed, Ellicott observes:
The emblem is not uncommon in the Bible. Invasion is described as "an
overflowing flood" (Jeremiah 46:7-8; Jeremiah 47:2; comp. Isaiah
8:7-8) The same emblem is used in Psalm 74:2-6 to describe the
uprising of a people's ill-will. The floods, the rivers, the waves of
the sea, are employed to express popular movements.