Anxiety can cause nosebleeds because when you're suffering from anxiety you're stressed out and when you're stressed out and are suffering from anxiety your blood pressure goes up.
When your blood pressure gets too high then your tiny delicate blood vessels in your nose can crack open and cause your nose to bleed.
The nosebleed is rare serious and usually goes away on it's own.
if your nosebleed continues and you cannot get it stopped then go to the emergency room or a walk in clinic to stop it.
It's unlikely that you'll bleed to death from a nose bleed unless it was really serious but getting it stopped is still important.
You can try pinching your nose shut or tilting your head back and eventually the nosebleed should stop.