Putting aside the fluff about candles and bubble baths, self care is everything we do to look after ourselves. It includes going to bed at a reasonable hour, eating food and having a shower, as well as the what might be thought of as "upgrades" such as a night off, a fancy bubble bath or a spa day.
We aren't machines, but the analogy is similar enough - we need certain things, in enough quantity and enough quality otherwise we break down. We don't expect a car to keep us motoring without fuel, oil, a service and an MOT once a year, and fixing the things that break properly, yet we expect it from our minds and bodies, which are much more complicated than a machine.
In my case I expected my body and mind to carry me though without enough rest; not just sleep but quiet down time. I didn't give myself that, because I thought I didn't have enough time(!) and I burnt out in 2018 and now have a chronic fatigue condition as a result.
I promise you that if you don't make time to do it on reasonable terms, your body and mind will break until you have to do it on unreasonable terms.
If you are expecting more from your body and mind - like the OP is, because she has a LOT on her plate - you need to put extra in, or you will break. Better quality food, better quality and sufficient rest, better quality off loading of mental and emotional burdens like counselling and therapy as well as letting off steam to good friends.
Unfortunately as everybody who HAS ever experienced burnout will testify, the least likely person to acknowledge they need to up their self care is the person who is well on the path to burn out, because it sounds like just another thing on the to-do list, and at that point you think you're invincible, you don't think you have any choice, and you see looking after yourself as a luxury you can't afford. I sympathise entirely, like I say, I have been there 
Unfortunately though, self care isn't a luxury. It isn't pretty linen and bubble baths. I mean, it can include those, if that's your jam. For me it looks like weekly therapy, dropping some of the things I'm juggling regardless of if I think they'll smash if dropped or if anybody else will catch them. It looks like a kitchen timer to tell me to get off the computer after an hour. It looks like ready meals half the week, because though I enjoy cooking, I now understand my energy availability better (See: spoons theory). It looks like a rule to have fresh fruit or veg with every meal - I keep bagged salad and bought smoothies for the times when meal prep is a spoon too far. It looks like switching my phone off at 10pm. It looks like saying no to some things that my elderly parents I am a carer for, want me to do. It looks like outsourcing as necessary - they now go to the chiropodist for their feet instead of me doing a bad job of toenail cutting, and get their prescriptions and groceries delivered instead of me getting them. It looks like knowing my limit for how many hours I can spend on Zoom, and also choosing to send my child in a taxi to his sports training without guilt (I pick him up). It looks like getting a cleaner, when that's possible. I have a gardener, and it's the best £15 I could spend.
It looks like saying no to a lot of people and things that I used to say yes to, because I know that I simply do not have the energy to do it all without getting sick, properly sick. And I'm terrified of that, because I've been there and I promise you if you think you can't afford to drop any of the plates you are spinning now, when you burn out you will understand that they will all fall and smash if you don't take self care seriously.