Praise be to Allah.
If the matter is as described then your fast is valid, because your getting a nosebleed was something involuntary so the fact that it happened does not mean that you broke your fast. This is indicated by a great deal of evidence from sharee’ah, such as the verses in which Allaah says (interpretation of the meaning):
“Allaah burdens not a person beyond his scope”
“Allaah does not want to place you in difficulty”
And Allaah is the Source of strength. may Allaah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote.
Standing Committee for Academic Research and Issuing Fatwas
Fataawa al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta (10/264, 265).
It also says:
If a person has a nosebleed involuntarily whilst fasting, his fast is still valid. End quote.
Fataawa al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta (10/268).