Some capillary bursting is normal. It goes away over time, as the weak capillaries get replaced by stronger ones. Half of the eyelid turning red is a little extreme, though.
Feeling like you're about to faint after deadlifting isn't normal. That feeling comes from a very quick drop in blood pressure, and can be alleviated by bouncing up and down to slow the blood pressure drop. Are you doing something strange like dropping the bar?