Hi Fangirl,
Your post resonates with me as I feel many of the same things. I also struggle with making friends, so have very few. I feel like I want to hang out with them much more than they want to spend time with me, which makes me feel like a burden on them. And I feel so disappointed if they are busy and I can't see them.
I am doing uni online, though am dropping some of my subjects as it is too much for me. I feel really hopeless about my inability to manage a full time load. I wonder whether there is any point me studying, as I don't know whether I will ever use my course to get a job, if I even finish the course. But at least the course does give me something to do and think about. I do find some of it interesting & I feel that at least I can say I am studying to explain why I am not working, which is a slight boost to my self esteem.
I agree having a pet is so therapeutic, especially when alone. My dog passed away unexpectedly 1.5yrs ago and I was really devastated. The only way I could fill that aching hole inside me was to get another dog. For about a year, I had difficulties bonding with the new dog, as I missed the previous one too much. But after a year or so the pain had lessened, and I realised I did love my new dog, even though she was so different. I still have beautiful photos and memories of the dog I lost. It must be difficult for you to know your cat is unwell, but savour your time with him/her and take some photos that you can look back on. I found people so much more understanding of my grief when my dog passed away, than of anxiety or depression. Have you tried Griefline? They have a helpline that I found useful & their website is ok too. Remember it is natural to grieve over someone you love, especially a pet, especially if you are alone, and even if they are still alive.
No one deserves mental health struggles. Try to do what ever tiny things make you feel a little bit better. A nice treat to eat for you and your cat, a scented candle, reading a book your enjoy, or some other hobby. You deserve to feel good. And perhaps your hobbies could help you connect with others. I like reading and go to the library often to change my books and enjoy talking with the librarians. They are not friends, but still nice. When I took up knitting to fill my empty days, I was surprised at the possitive comments people made about what I had created, as I felt that I couldn't do anything worthwhile. Other way to have contact with people is volunteering, you can meet nice people who want to help in the community, and it might help you feel more worthwhile. Perhaps helping with elderly, children's groups, animal shelter, fundraising, charities or whatever interests you.
Good luck with your counsellor & psychologist. And remember if you want someone to talk to - Lifeline or other helplines are happy for you to call. At first I was really afraid to call any of these numbers, as I felt they were for people whose problems were much worse than mine. But now I am ok with calling if I need a bit of extra support.