What’s the longest a toddler can go without sleep

My toddler seems to be fine with 4 hours a night and sometimes a nap for 3 hours. It sucks for me though because I’m running on no sleep. We have a schedule and routine in place but he just has so much energy and is fine not putting in extra sleep hours. I’ve become a MEAN MONSTER. & I screamed at him GO TO SLEEP two times on top of my lungs and it scared him and made him cry but I’m so miserable not getting any sleep at all. & no I can’t get help by anyone. I hope that occasional screaming doesn’t mess him up emotionally/psychologically. Will he be OK? I don’t want him to hate me now. On top of that he is drinking 10 bottles 9oz of toddler formula through the night. He eats fine throughout the day too so he isn’t hungry. Maybe it’s habitual. I also hand him the tablet to keep him calm so I can catch up on sleep but he still smacks and kicks me to wake up because he doesn’t want to see me sleep but still wants to watch videos on his tablet so the tablet idea does not work for me to catch up on sleep. I’m not worried about him not getting enough sleep since he seems to be pretty content overall which I’m thankful for but I’m the one that is cranky and cannot be a good parent without getting some sleep. How can I be a good and sweet mom without getting sleep???