Great post and good idea making a fun thing that you do with your toddler.
I also thought.
Are you are overwhelmed by all the things you have to do that you don't know where to start. Or overwhelmed by choice? Or you are punishing yourself in some way because you feel you don't deserve these things or you are worried about the future? Or you feel that you need permission because it feels like splurging and you don't deserve it. It might help to ponder on what it is that makes you reluctant.
It sounds like you don't have much real life support. You are a single mum with a little one, it can be tiring and demanding and difficult when you have so much to do that you don't know where to start. It can be lonely too. Depending on your area, there are places that will help, have a google or maybe there's some suggestions on this thread. I thing you should see GP and find out what support is available. Or if you could have a trusted friend/relative to help or even hire a professional organiser.
The good news is you have enough money to pick somewhere online like Sainsbury's, Argos, George at Asda or Amazon today and just order cooking utensils, oven gloves, a set of towels and a simple white duvet cover. These are relatively cheap and so even if you feel you've made the wrong choice, you can send them back or just buy another. You could order them all in one go. The sales are on. Then they would just turn up at the door and it would be one immediate improvement in your life. Then you can think about what else is needed. Just pick them out. Put them in the Basket. You don't have to press go immediately, but you've highlighted these things as missing so you can justify buying them.
You deserve this. It's also about safety for your son and yourself - you could seriously burn yourself not having an oven glove.
When I had my first home, I was literally overwhelmed by the amount of stuff to do after work with kids. I used a website called Fly Lady and the idea was that things don't get into a mess overnight... and so you cant fix it overnight, you need to take everything step by step so that it doesn't overwhelm you. there are tonnes of inspirational videos online now on how to do this which are more modern. I'm sure people will have suggested them on this thread. My parents could not be described as homemakers in any sense (continuous half finished building projects, reluctance to buy suitable furniture, saving objects they didn't want/need) and I really didn't have a clue at the time, but these online things helped so much. I also think it would set a good example to your son, in helping to teach him how to make the home more comfortable. I know his rooms are nice but he will pick up so much for seeing how you organise your own space.
The first steps in that program, were things like setting a timer for 15 minutes and just cleaning the kitchen sink or grabbing a bin bag and putting all the rubbish in from one room. Because they used to say you can do anything in 15 minutes. It won't overwhelm you and you will start to see a real difference in less than a week. You could start with all the stuff you mentioned to throw away in your bedroom.
We moved into a house with zero storage and I can completely identify with piles of books and clothes and no where to put them. Its can be time consuming and draining on top of the other things you have to do and also hard choosing what to buy to fix it. But you do have substantial savings so its not going to drain you to buy a wardrobe. Just pick one to be going on with, one for now, think of it as a temporary measure, you don't have to keep it for 20 years. Sell it if in a few years and upgrade. People do that all the time. Remember its in your room and so no one will see it unless you want them to. No one will judge you for your wardrobe choice. If you can't face that immediately. George at asda online have hanging rails for £20-30 so at least you can hang up and sort your clothes whilst you decide. Just having them hung up with make your own bedroom seem like less of an unwieldly problem area.
If you are struggling to pick a style, pick minimal and you can always upgrade and add things later. Eg. Pick a wardrobe that is delivered ready assembled or pay for someone to assemble it or it will never get built. Dreams have a sale on and we've just bought a very comfortable mattress/bed on interest free. Its all online so you can check it out. Wayfair, Dunhelm, John Lewis all have nice beds. That is quite a large item so maybe just start with a nice plain Duvet cover from JL or M and S, and get it delivered.
These are little fixes that won't cost that much and can be ordered relatively simply. Why not try doing one batch a week and see how you feel about it?
Also Don't beat yourself up about your situation. You are doing your best with your current energy and resources and the first step was assessing the problem and writing it all down here which must have taken a lot of courage. You sound like a kind and caring mum, and I hope you can direct some of that kindness and care towards yourself too.