Stress is at an all time high and if you need a mental health day, take it. Tell your boss the truth, or don’t and say you’re sick (sick of work is how I see it).
I’ve had to explain this to multiple people at work who try to everything to come in to work even if they aren’t able to get things right at home. Fuck this job. Your mental health is miles more important than anything here. This can wait, your health can’t.