Hey Violet
You reminded me of several things. That before I ever found alcohol, my primary diagnosis when I was only 14 years old was depression. And that is has been the task, part of recovery, to learn to live alongside it. And yes, as you describe, it can seriously get in the way. But I learned that this is not a reflection of my capability, it is that there is this impediment, that is sometimes there, and sometimes not, and we respect each other these days. You said in your post something very important, about being able to do only a little, and then needing to rest. It is so important that rest, real rest, without fretting about all that is not getting done. So do rest, do be gentle with yourself.
As others have suggested, a visit to your doctor may be useful. In the short term, medication can help clear the mind enough to get through tasks, and is a practical step to take. Action always helps, particularly where depression can leave us feeling helpless and overwhelmed. The simplest of actions can be a demonstration to ourselves that this thing is too much to handle alone, but today, we took courage, and spoke with someone about it. Similarly, if you are studying, there may perhaps be a college counselling facility you can make use of, and for me, the simple relief of letting out all the concerns and frustrations, helped greatly. It's not that there was an instant solution, but there was somewhere to take it, and let it out. It also made it more possible to ask for help elsewhere, from college tutors, because I could articulate more clearly why the work was behind, and what support I needed from them, rather than getting further behind, and just ruminating on it by myself. Likewise, some employers (mine does) offer employee support over the phone, and can offer counselling sessions.
Now, it can be very hard, as you described so beautifully in your post, to focus , to concentrate, get things done, particularly to read, and I'm a great reader. Two books that greatly helped me with depression; The Little Book of Beating the Blues by Cheri Huber (so practical, so compassionate, and very short) has been a guiding light for me, and if you like a story, Mr Chartwell by Rebecca Hunt, which brings to life Winston Churchill's depression, which he referred to as his black dog, in the form of a dog called Mr Chartwell, who visits himself on a young woman. It is funny, and touching, and charts a journey through what an experience of depression can be like.
Despite how you are feeling, your post makes it clear you continue, however slowly or falteringly, to put one foot in front of the other. Don't underestimate the courage that takes.
Wish you well, and hope you find the solutions that work best for you.