Tired?

My son is a month old and doesn't even cry when he's hungry or has a dirty diaper he starts grunting and I feed and change him than he looks so tired so I rock him he gets fussy than that turns into him screaming he will stay up for 6 hours at a time I can calm him but once he's sleeping that last maybe 30 mins than he wakes up crying. I feel like he is so tired and he gets angry. This isn't all the time but almost at least once a day.