What is the ruling on someone who swallowed something that came out of their stomach, thinking that it would not break their fast, then discovered the error of their action, and does not know the number of days they did that?

As long as you did not know that swallowing this food breaks the fast, you are not required to make up for it. This is because ignorance of things that break the fast is an excuse, according to the soundest opinion. Therefore, if a person eats out of ignorance, they are not required to make up for it. Ignorance is of two types: ignorance of the ruling and ignorance of the time. This is supported by the Hadith (definition) of Adi ibn Hatim (may Allah be pleased with him) regarding ignorance of the ruling, and the Hadith of Asma bint Abi Bakr (may Allah be pleased with her) regarding ignorance of the time.