What is the ruling on boils, if they are not on the organs of ablution, and blood continues to flow from them without stopping? And is it obligatory to make up the prayers that were performed in this state?

That which flows from boils without squeezing or peeling is excused, or if there are multiple boils, even if the person squeezes or peels them. However, if it is a single boil and the person causes the blood to flow, it is not excused unless it exceeds the size of a Dirham. Inseparable impurities, such as boils, are excused. Therefore, your prayer is valid.