Ok so because it’s under your eye (idk if this is true but based off what I know) there are many receptors under your eye that cause you more Intense pain so it’s best if you get some tissue or any bandaid and hold it under your eye until the bleeding stops
Try um uh put something over it, make sure to put medicine on it by he way just in case no infection gets in, if it's bubbling then try to get the blood out please, it may hurt, but um yeah if itd bubbling hsts infection. Once that's gone out medicine and a bandaid on