Hey Gray, it's nice to meet you. My name is Luoma. I'd firstly like to welcome you to the forums and to SF in general.
Next, I just want to say I am so sorry that you are feeling this way. The truth of the matter is that a lot of the time, mental illness can get in the way of doing the things we want to do. Whether it's important stuff like school and chores, or not so important stuff like moving boxes or other small tasks, mental illness can take any activity and make it as hard as scaling the highest mountains. However, like the highest mountains in real life, we do not expect to overcome them in one simple step. It takes a lot of work and sometimes it is very difficult, though the end goal can ultimately be achieved. It is natural for us, as humans, to wish to accomplish things and to want to get stuff done. But I want you to remember that if you're sick, either physically or mentally, you cannot expect yourself to do absolutely everything during the day without having any tiring thoughts. It just sometimes isn't possible. You have to be kinder to yourself and let yourself know that it's not laziness that drives you to not do these chores, but rather, mental illnesses, and you should remind yourself that.
Getting therapy and medication, for a start, is the best way that you can fight out the negative emotions. I also want to really look at what you tell yourselves while doing these tasks. When you have a dark thought or question in your mind, question it back. For example: "If I keep doing this, I won't have free time." Reply: There is always time to do things, whether it be today or tomorrow. "I can't do this." Reply: I am trying by best and will keep trying, I know my body can do this. "Do I have to really do this?" Reply: Yes, and so does everyone else. This is life. The sooner I finish, the sooner I can have free time.
It's all about balance, but not balance as in half and half. Balance as in for x amount of time doing chores, I do y amount of thing cleaning. It's about recharging your batteries. A few chores might really drain you and you might need to do more relaxation to get your mind back into a more stable place.
Also, not sure if you were specifically speaking about chores, but just letting you know that if reading books makes you depressed, just don't do it. Do things that make you happy. And as I said before, remind yourself that your mental state can be a huge roadblock as to how willing you are to do things. Some days I am so depressed I don't even want to get out of bed. So it's all about how your brain works.
I'd suggest speaking to a professional; they can really equip you with tools to fight the whole 'not wanting to do anything' thing.
Best of luck to you!