Firstly, I wanted to say that I’m so sorry things suck for you right now. You’re having a really shit couple of months, sounds like! I’m keeping my fingers crossed that things start to improve for you soon - a month without suicidal depression is pretty good, definitely sounds like things are heading in the right direction!
I don’t have experience of med-related fatigue, but I’ve a 10-month-old baby who doesn’t sleep much. And didn’t sleep hardly at all for the first 6 months. So if that kind of sleep-deprivation is at all relevant (your description of it being like you’re drunk sounded remarkably familiar!) then I second the advice to cut things back to the bare minimum for a while. It won’t be for ever, and it doesn’t mean you’re incapable or under-achieving, or never going to be a proper grown-up again. (The last might be my own issues, there. It’s definitely something I remember wailing at my husband in the midst of a particularly bad sleep week.) It just means that you need to concentrate on making sure you’re physically and mentally solid before you can build on that to do other things - that whole hierarchy of needs thing.
You will probably start to adjust to the meds, so the fatigue will lessen. But until then, I’d make a list of stuff that needs doing, in order of absolute urgency. Give yourself permission to do one (maybe two) of those things a day - if you’re feeling up to it - and don’t beat yourself up if you don’t manage it. Just try again the next day. If you’re having a good day and manage more, then bonus! Are there any things on the list you can get someone in to help with? We have someone who comes and does the cleaning for us, which is an absolute godsend - if we had to rely on me, we’d have been living in squalor for at least the first 7 months after the baby was born. Is something like that an option? I felt (briefly) bad about doing this, since I ought to be able to clean my own bloody house, but then figured that if I were at work and had stuff I couldn’t handle on my own, I’d delegate it or get a colleague to help me out - this is broadly the home equivalent, in my mind.
For keeping yourself awake to do the things you absolutely need to do and can’t get anyone else to do for you, maybe a cold shower? I find those wake me up for a while at least. If you’re in an office and that’s not possible, maybe just splashing your face regularly with cold water? Going for a walk outside helps a bit, too, if you can manage it. Also drink lots of water - and are you eating regularly? Small, more frequent meals might help.
Good luck - you can do this. You’ve got through worse things, you’ll totally manage this. But you’re not well at the moment, so I wouldn’t try to achieve everything you would if you were 100% on form - it doesn’t mean you won’t get there in the end, but take it a bit slower for now. Be nice to yourself - you’re doing the best you can right now.