Hi OP, I'm not sure I can give you huge words of wisdom as to me you already sound pretty much like super-woman, you are managing to raise a DD with SEN, recover from MH issues and keep on top of it, be a nurse, study for a degree, maintain a relationship and be on good terms with your ex all through a pandemic, that sounds pretty impressive as it is to me, bloody well done 
! I do have a little bit of experience though with some of the things you mention as things you'd like to change as I've previously lost a bit of weight (and so far managed to keep it off) and have had to 'teach myself' budgeting and how to keep a clean and organised home as I came from a somewhat chaotic family background where these things were not really done/taught...
One thing that did strike me was you say in your title and post that you want to 'start a new life', when I clicked I thought it was going to be about emigrating to the other side of the world or having a total career change or something. Whereas actually for things like eating healthily, staying more on top of your house and finances, in my experience what actually works is small, sustainable changes rather than dramatic overhauls. Don't get me wrong, I used to think like you and would imagine that whatever new regime I was putting in place would lead to a whole new me, my life being totally different, e.g. going from living in mess, clutter and dirt to show-home perfection, and that if I only put the effort in surely the result would follow, but that was way too much expectation to put on myself and only led to a shame spiral where small failures seemed to lead exponentially to total abandonment of the plan and ending up back where I started or worse! I also think it was linked to poor self esteem where I thought my life was basically inherently terrible and I was a bad/lazy/slatternly/greedy person and that got into a bit of a loop because where my underlying belief was that I was that kind of person, I expected that I would behave like that kind of person, and would kind of sabotage any attempts to change, if that makes sense? It took a bit more maturity and understanding of myself and the realities of life, that actually everyone struggles with these kinds of things, no-one enjoys doing chores (or well, maybe some freaks like MrsHinch do, but the vast majority not!) or being sensible with money, it wasn't that I am some kind of unusually useless person, it's just a case of getting into a routine and a position where it is easy-ish to keep on top of these things and that doesn't happen overnight!
So I think I would start off by being a bit kinder to yourself, rather than picking all the ways in which you feel you've failed and need to completely be 'kicked up the arse' and changed, I would think more about building on your strengths and doing things which will bring you pleasure or relaxation or tangible benefits. Also about picking one small thing, changing it, and then only when you have proven to yourself you can stick to that thing, picking the next one.
I am a big fan personally of things which are structured, lists, checklists and spreadsheets etc. So for the housework possibly you could look into The Organised Mum method, FlyLady or UnFuck Your Habitat - these basically all do the same thing by getting you into a routine and structure with your housework on a little and often principle which basically is what works, naturally I would incline towards doing a massive exhausting blitz of the house for a whole day, getting everything sparkling clean, every single item of laundry done etc and then slumping into an exhausted heap and then doing nothing for weeks on end. This is not a great way to do things! It's much more boring but miles more effective to do 20-30 mins per day every single day no matter what else is happening in your life. It's not much fun but I put a podcast or music playlist on that's roughly that long, I clean/tidy for the length of the podcast and then stop when it's over, but do that every.single.day. This somewhat mitigates the dullness of repeated chores, and also my somewhat manic tendency that once I've started e.g. tidying I feel I can't stop until every single thing is in it's place - sometimes good enough is enough!
Similarly with budgeting, it's quite dull but what seems to work is structure, understand your income and then account for all your outgoings and see if/where the two don't match, there are various apps such as You Need A Budget which can help with this or I just use a simple spreadsheet. MoneySavingExpert has a great 'audit your finances' tool as well, and very helpful articles/forums. But I think given that you are studying for a degree at the moment, which presumably you are hoping will lead to a pay rise when you are finished, maybe finances aren't number 1 priority right now (obviously if you are so far in debt you are about to lose your home or go bankrupt it might need to be!)? Although there may be some quick wins you can do such as going through your direct debits and cancelling any subscriptions and memberships you don't use or switching energy or insurance providers to get better deals?
For diet I would possibly look at easy swaps you can do without feeling like it's a sacrifice, things like diet fizzy drinks instead of full cal, swapping out junky snacks for healthier ones, or perhaps changing around your meal times if you find you are snacking at particular times of the day? You could make healthy eating a bit of a project with your DD, depending on her age, you could learn to cook some healthy meals together, don't abandon the things you like to eat totally but if for instance you are having a lot of takeaways you could look into making your own 'fakeaways' which will save you money and be healthier too? Or try baking homemade treats together? Or perhaps can you start a bit of exercise (I appreciate time may be an issue and getting outside in the current weather and short days is difficult), but something like a daily walk, even a short one, will have a lot of physical and mental health benefits!
As I say, it sounds like you have a huge amount on your plate right now so don't put pressure on yourself that you need to do all this right away, if what it takes to get you through is the occasional treat or takeaway then do it and enjoy yourself, but look at where there are easy/silly things that with a bit of planning and organisation life can be made easier and better? Good luck! 