I don’t do 12.5 hour shifts anymore, but I take my hat off to you doing it with two young kids and not much help. I found when I did long day/night shifts it was really hard to keep any form of a weekly routine, or even know what week it was, and I had to plan way in advance to keep up. Some rambly random tips aimed at making life easier:
I use the calendar on my phone to write reminders for everything, car insurance renewal, birthdays (I save a reminder with their address five days before their actual birthday so I remember to post their card), to text a friend “good luck” for a job interview or scan etc, everything.
I buy birthday cards for everyone I know once a year, and keep them in a box with stamps and couple of random new home, engagement, baby and wedding ones.
Declutter EVERYTHING and apply the “toothbrush principle” to everything: everything needs to have a home and live there. This takes time, and you might need to invest in more storage, but is so worth it. Try doing 10 – 15 minutes of decluttering a day for the next month or so, and be ruthless; if you haven’t used it recently then get rid. Life is much easier when you have less stuff. Google “decluttering challenge” for inspiration, find one you like the look of and try it. Better to do little and often so it’s less overwhelming, set a timer to keep you focused.
I also like TOMM, I have the app and have altered it quite a lot now, but I like the idea of the level one and two jobs, and love the playlists on spotify. My level one jobs are: make the bed, wipe down the kitchen worktops, hoover the kitchen for a minute (usually while the kettle boils in the morning), and give the bathroom a two minute clean (usually do this straight after brushing my teeth in the evening). I love that Gemma’s motto is “there’s more to life than housework”, so true. If you look up the organised mum on insta, she posted something about how it’s impossible to have/do it all; something has to give if you try to do too much, so be easy with yourself.
On your days off, do the chores that you don’t enjoy first thing to get them out the way. There’s a quote by Mark Twain that goes: “If it's your job to eat a frog, it's best to do it first thing in the morning. And If it's your job to eat two frogs, it's best to eat the biggest one first.” Basically it’s best to do what you don’t want to do as soon as you can so the mental load of it doesn’t have time to build up through the day and seem overwhelming. Set a timer and tell yourself you only have to do 30 minutes, or just 10 minutes if you are struggling to get motivated, it’s surprising how much you get done in 10 solid minutes.
Listen to music, audiobooks or podcasts while doing chores you don’t enjoy (try not to have tv on as it’s easy to get sucked in to sitting down). Focus on getting it done and then enjoy your guilt free day off.
Get an audible and Spotify subscription for the above.
Get a cordless hoover and spray mop.
Get a “crap basket”, maybe three different ones for you and both of your kids, then when tidying in a hurry you can just chuck stuff in there and get them to sort through it later.
Only have black socks that all match each other.
Don’t have a laundry basket; dirty clothes go straight it washing machine, and it goes on when full. If it has a timer, programme it to come on so it’s done first thing in the morning (or when you get up if on nights), put everything on for an extra couple of spins so it dries quicker.
Don’t fold anything; if you have space then buy a clothes rail and a load of hangers, everything goes on a hanger straight out the washing machine, then straight onto clothes rail.
Rotate summer and winter wardrobe: go through everything around May and October, and donate/throw things that you no longer wear or are worn out, put the out of season stuff in vacuum storage bags and away. Gives you more room in your wardrobe and easier to see what you’ve got.
Meal plan for a month. Once you’ve written out a meal plan with the matching shopping list, you can reuse it without much thought. Saves time and money.
Batch cook, and think about getting a chest freezer if you have space for one. I used to have one and loved it, when I did long days I would plan to spend one of my days off at the start of the month batch cooking a load of meals for dinner, things like chilli con carne, curries, lasagne, pasta sauces, stews, shepherd’s pie, soups. Solids went in reusable plastic containers, liquids in freezer bags that were frozen flat. Everything labelled and dated (bit of masking tape on reusable containers), and then I would write a list of what was in there and cross it off as I ate it, so it was easy to know what was in there. I also used to have a load of frozen veg, chips (sweet potato ones are healthy right) and fish fingers etc in there for when I just wanted to chuck stuff in the oven. But on the monthly batch cooking day I would motivate myself by telling myself if I did it all now it would just be a case of reheating it for the rest of the month, and would have something on to binge watch in the background while I cooked.
Get a slow cooker.
Take vitamin D.
Try to keep a routine (as much as you can with the shifts) and get a little bit of exercise every day. You mention in your OP that you have no energy and you’re not sure if it’s a hint of depression, I have recently been quite depressed, and found keeping a routine and making myself do a little bit of exercise every day, even just a ten minute walk, has been really helpful.