My child used to have severe nosebleeds. One night I was trying to stanch the flow using tissues without much success. Trying to keep a child still while pinching her nose is near impossible at 2 am! I happened to have a mini tampon in the drawer nearby so I unwrapped it and poked it just inside the nostril. It stopped the flow perfectly.
I told my doc about it and he said it was fine as it was sterile, absorbent and had the bonus of applying just enough pressure to constrict the blood vessel. The other bonus: it doesn't pinch the way rolled up tissue can.
Related: For the inevitable "bloody mess"