Neriz,
It does not make you a coward because you won't cut yourself..that takes a tremendous amount of strength to do. I am so sorry that you are going through so much right now. Sometimes even the smallest tasks can seem completely overwhelming.
Just try to look at the small things that you accomplish. For example you went food shopping today.. so look at the as being a great thing instead of dwelling on all the wrong things that happened today.
Depression can make us feel like we do everything wrong and does not let us look at all the wonderful things that we do right. Try not to look at the big picture all the time.. it can be too overwhelming.
I do not know if this helps..i just wanted to let you know that I read your post.

Jessica