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 is His slave and Messenger.
You are not obliged to perform Ghusl again because of this blood because it is not menstrual bleeding, which entails Ghusl. Scholars underlined that the menstrual bleeding is that which comes out by itself (without a cause). Mawaahib Al-Jaleel reads, "It comes out by itself (without a cause); this characteristic excludes the following: the post-partum bleeding which occurs because of giving birth, the bleeding which occurs because of the breaking of the hymen, and the vaginal bleeding outside the menstrual period which occurs because of a specific reason (like an illness or the like)."
Hence, you come to realize that the blood that came out because of the breaking of the hymen is not menstrual bleeding and does not prevent you from performing the prayer and reciting the Quran. However, this blood is impure and entails performing Istinjaa' (cleaning the private parts with water).
Allaah knows best.