Hi Smacky,
I have heard these same words from my husband, he has major depression/anxiety/OCD. He has that feeling of worthlessness also, even though to others he is extremely valuable. I love him and have for over 30 years. He is in counseling now and he has learned that he like you gets his own value from the things he accomplishes instead of who he is. Therefore if he isn't sucesseful or accomplishing anything he doesn't feel he deserves to live. It's more complicated than that of course as I'm sure it is with you. But that is at least part of it. Try to change your thinking to you being worthy just for you. Don't let school, career, or other externals define your worth. You mention your family, reach out to them. If I was your mom I would want to know what you are going through. Chances are someone in your family has struggled too. They may be able to help. Swim to the surface, let the sun shine on your face, let that be enough for now. You are a miracle and I can tell from your post that you are very smart and thoughtful, you are not a waste of life in my book!