OP, please see your GP. I was where you are now 5 weeks ago. All the textbook symptoms of stress - headaches, insomnia, gut problems, irritability, rage, crying ALL the time (I started switching my camera off for meetings as I couldn't trust that I wouldn't start crying), no decision-making ability, forgetfulness...I was so overwhelmed and was not a nice person to live with. My poor DH and DD (8) bore the brunt.
Anyway, my husband and best mate nagged me to see the GP, so I did. She signed me off work for 4 weeks with Stress and Low Mood. First time in my 20 year career that I've been signed off. She was just so lovely and supportive, as were my work. I've had 4 weeks to "reset" myself a bit, and yes there has still been homeschooling and all the domestic grunt work to do (husband also works shifts so I'm flying solo much of the time), but by removing a large part of that stress I have been able to catch my breath and recalibrate a bit.
I've returned to work this week - it's a phased return, 3 days this week, 3 next week and then back to FT. Workload is lighter and everyone has been so kind and supportive. I'm a bit older than my boss and colleagues- it's clear to me that the Millennials and Gen Z-ers are just so much more sympathetic than my generation to mental health hiccups - I was initially fearful of the affect on my career, but I realise now that a) that view is pretty outdated if you work for a half-decent employer, and b) I don't actually give a shit and that my health and my family's happiness is waaaay more important, and that I'm not going to lie on my deathbed saying "you know what? I wish I'd worked a bit harder".
See your GP, get signed off and give yourself a break. 