I read your query carefully and I understand your concern.
There are many possible causes for
nosebleeds, most of them fairly benign, related to irritation of nasal inner lining due to a
common cold, fragile blood vessels etc.
Rarely can the acute pain of
migraine increase the blood pressure so much that it can cause a rupture of the superficial vessels in the nose and bleeding. Also
high blood pressure due to other causes could cause the same thing with the headache being as a result of the high blood pressure.
So unless you have some other symptom or repeated bleeding, I wouldn't panic and for the moment would limit evaluation to repeated blood pressure measurements for a week (at rest, without taking caffeine or other stimulants in the preceding half hour). If high values are found then you need to see your doctor to investigate the cause.
Also routine blood tests like
complete blood count and liver function tests can be done to check for coagulation abnormalities.
I hope to have been of help.