I can’t make a diagnosis on the basis of a letter but what you are describing sounds very much like symptoms of depression. Feelings of hopelessness and helplessness to change; getting no enjoyment from what used to be enjoyable activities, and difficulty concentrating are all hallmarks of depression. That being said, you are also talking yourself into a belief that you are a mistake – which is going to color everything you think and do. Yes, you are 12 years younger. Has it occurred to you that maybe your parents wanted another child for 12 years and were happy to finally have you??? Even if you weren’t planned, it doesn’t mean you are a mistake. Your parents decided to keep you, didn’t they? Sometimes unplanned babies are wonderful surprises. They give parents another shot at being the kind of parents they want to be. They bring joy to parents’ older selves. You have all the advantages of an only child — with experienced parents and a sibling. Sounds pretty good to me. Maybe a little chat with your folks would help you understand the positives from their point of view.
If your parents don’t know your favorite color, I wonder if you’ve told them. At 19, it’s time for you to stop expecting your folks to be mind readers, to start letting them in on who you are, and to work on getting to know them on another level. It’s also past time to tell them the truth about what you are feeling and to ask for some help. Your beliefs that you will fail at whatever you do will sabotage even your best intentions. You need some help getting out of your rut and back on track. I suggest you find a cognitive-behavioral therapist. CBT will teach you how to stop the negative thinking and replace it with a more positive self-image. It will give you tools to start accomplishing something more to your liking than a record of failures. It will teach you how to take more risks with friends and family so they can get to know who you really are.
If you could have fixed things on your own, you would have done so long ago. I hope you will follow up and find a counselor for yourself. Take a look at this website. I don’t have personal experience with the listed counselors so I can’t offer you any guidance about who to contact but the site does look like it might be a good place to start your search.
I wish you well.