when i told my kid off too harshly

so this thing happened a while back. we were having one of those days where everything feels like it's going wrong and everyone is just so tired and cranky. i was trying to get the kids ready for school but my son, let's call him alex, he was being really stubborn about putting on his shoes and getting dressed properly. i swear sometimes he's just being a kid and pushing buttons for kicks. we've had similar arguments before, nothing too serious, so i thought it would be one of those days where if you just breathe deep and give in a little bit maybe everything will go better. but this time, something snapped. like all the frustration built up finally reached its boiling point. i yelled at him to hurry up or he was going to miss the bus, that sort of thing. we both knew it wasn't true because i can always call and get someone to pick him up if he's late. but in that moment it just felt like everything had gotten so out of hand, like there was no point trying anymore. i said things like 'why are you making this so difficult', 'what is wrong with you'. stuff like that. afterwards, i could see the hurt look on his face and then he just walked off to his room, slamming the door behind him. it's been a few days now and we're both still kind of walking around with eggshells between us. i've tried to apologize but it feels so heavy, like those words just aren't enough. i keep wondering if saying sorry is even helping or if what i said has already done some damage that won't be easy to undo. the thing is, i really do love him and want the best for him, but sometimes being a parent means you have these moments where it feels like you're failing in the biggest way possible. maybe this one will just stay with me until he's old enough to understand that his dad was just having a bad day.