I ask for a Mental Health Day, how do I not feel guilty about it

I have been so burnt out from full time work, full time graduate school, and also doing supervision fieldwork. In addition of keeping a relationship that is slightly falling apart, keeping myself healthy through multiple chronic diseases…my work is basically working with highly aggressive clients.

Anyway, my dog was sick last night and I had maybe a total of 3 hours of sleep just to wake up at 4 am to be in an online class that’s in EST not PST.
I told my boss, my clients families, and put in a PTO request to be like “look I don’t want to be written up but I can’t function so here’s the very little PTO I have to use for today”

I won’t get a response for another 3 hours since they don’t start work until 9am, I start at 8am.

When I told my boyfriend, he said I shouldn’t have used my PTO and just pushed through. So I feel even more guilty for asking off just for a mental health day of burnout and sleep.

What do yall do to not feel guilty over asking off for what feels like a valid reason?