Sleep deprivation is making me weirdly emotional

My daughter is 6 weeks old and I think I'm losing it. Last night I almost cried during a diaper commercial at 3am. My wife laughed at me which obviously made it worse. Is this normal or should I be worried? I've been doing the midnight shifts while she handles early morning so she can sleep a bit longer. Honestly I can't remember the last time I slept more than 2 hours straight.