I haven't been able to sleep lately because I've been taking care of the baby, so my skin is all messed up ㅠㅠ

These days, I'm really feeling what it means to not have time to look in the mirror.

My baby has been having teething problems lately, or has been having gum problems, so he hasn't been eating well and keeps waking up at night crying, so I've been forced to stay up all night too. Since the day and night cycle is reversed, his skin is naturally dry, and he's even started getting a few pimples under his chin. I haven't had time to put on skincare, so I just wash my face and slather on some moisturizer, but it feels like his skin barrier has completely collapsed. I really respect people who take care of their skin while raising children. How do you all treat sleep deprivation?