Can I fall asleep again tomorrow after doing it today in class while the teacher was talking?
You didn't! What made you fall asleep?
I had a hangover from the night before.
You really shouldn't get drunk the night before work or school. Falling asleep could get you in trouble or even fired or expelled. You should save that for when your free the next day.
I'm just not a morning person, it's my character.
Weather or not you are a morning person or not, control the urge to drink the night before a school or work night. Take it seriously because your life depends on you being sober enough to do things right.