All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ʻalayhi wa sallam, is His Slave and Messenger.
The scholars held different opinions on whether or not vomit is one of the things that invalidate the ablution and accordingly renders the prayer invalid. Please refer to Fatwa 84093. The view adopted on Islamweb is that vomit does not invalidate the ablution.
However, it is impermissible to swallow the vomit deliberately because it is ritually impure. Swallowing vomit deliberately during the prayer renders it invalid. The Kuwaiti Encyclopedia of Islamic Jurisprudence reads, “According to the Maalikis, if one is overcome by an insignificant amount of pure vomit and did not swallow any of it, his prayer is not invalid; but if it was impure or a large amount or one swallowed some of it deliberately, his prayer is invalid. If the person swallows any of the vomit forgetfully during the prayer, it is not rendered invalid and he should perform Sujood Sahw (prostration of forgetfulness) after the final Tasleem (at the end of the prayer). If the person swallows the vomit involuntarily, scholars held two different opinions about it. And belching up undigested food (Qalas) is like vomiting.” [End of quote]
Accordingly, you should know that there is no harm if the vomit returns to your stomach as long as it does not settle in your mouth. If it settled in your mouth, it is impermissible to swallow it because it is ritually impure. You could have hurriedly raised your head from Sujood and spat it out into a napkin or the like and placed it next to you. If you swallowed it due to ignorance of the relevant rule, you bear no sin for that, Allaah willing.
Many scholars maintained that the consumption of an insignificant amount of food or the like, as in your case, is excused and the prayer is not rendered invalid as long as it occurs out of ignorance. Ar-Rawdh Al-Murbi‘ reads, “The prayer is not rendered invalid by eating or drinking an insignificant amount forgetfully or unknowingly based on the general indication of the Hadeeth: "Allaah has pardoned my community of their mistakes and forgetfulness."” [End of quote]
Hence, you are not obligated to make up for that prayer; however, it is better and more prudent to make up for it so as to escape the difference of opinion and given the easiness of the matter.
Allaah Knows best.