You're bursting tiny little capillaries in the face and eyes. Capillaries are one cell thick.
Yes, since you're increasing your blood pressure to the point of bursting blood vessels in your face and eyes it could be happening other places too, but the major blood vessels in the brain (the ones you need to worry about when they pop) are much thicker and stronger than capillaries and even if a few capillaries in your brain burst it's not going to kill you.
I wouldn't worry about it. You would need a monstrous increase in blood pressure or some sort of condition that weakened the walls of your blood vessels before you're going to go dropping dead after a set of deadlifts.