Hi! It does sound as though you are depressed. The symptoms you describe are typical for depression and I have been experiencing them myself for some time now.
I binge eat when I am depressed. Even if I'm not hungry, I find the food comforting and it gives me something to do so I'm focusing on the food and not my feelings of depression. That means I have put on weight and so I feel bad about myself but, like you, can't seem to find the energy or motivation to do anything about it.
I am currently on antidepressants because I felt so low that I wasn't able to function properly. I was taking care of my little boy but not myself. I have been on them a month now and am starting to feel better. I wake up in the morning and my first thought isn't, "Oh God, another crap day..." which it was before. I'm not saying tablets are the only way forward but they can be a great help.
The most important thing to remember is that you
will get better, but it can take hard work. It might be that uni isn't for you. I went to uni at 21 and hated it. I don't regret doing it because I had lots of experiences that shaped who I am today but I ended up with a useless degree that I have never used. If you are sure that your course is right for you and uni is what you want to be doing right now then keep at it. See your doctor and talk things through with him/her. If you get an unsympathetic one go to another. Don't be put off.
Also, it helps to talk about things and get it all off your chest. It can be cathartic and help to clarify things in your mind. So keep posting here and have a good whinge if you want to.
All the best,
Jules.