Please realize that you are not a burden and your mother is trying to help even though its hard to take at the time. Know that you are among people who understand how you feel and know what it is to want to stay in bed all day hoping the world might just forget you. As annoying as it is to hear, exercise will help you feel better, but I know how impossible and painful it feels to even think about moving a muscle let alone getting yourself together enough to get out of the house. Simply getting vertical seems like a monumental task let alone tying your shoes or combing your hair. Hearing the words "why don't you go for a walk" are so painful and hurtful even though they are said out of genuine love and concern.
Although I am not a "cutter" I have an understanding of what it is that compells you to feel that way. Sometimes there is so much pain inside that it seems the only way to let it out is to draw blood.
The most important thing you can do for yourself is to get help. Stick with the dr's instructions and have some patience with the medication since it takes time to kick in. If you don't feel well - go back and have a check-in - maybe there's something else the dr. should know (like the cutting) that could help to find a better medication or treatment option.
See about talking with a therapist about all the things that are going on in your life. I see a psycologist every two weeks, regardless of how I'm feeling, and it helps a great deal since it is a good place to unload. Professionals are there to lend support and are a safe place to unload all the frightening things that run through our heads. They do not pass judgement, but can offer ways that might help to ease the pain.
Have patience with yourself and realize how much the people around you care. Its all about baby steps. Maybe exercising seems impossible, but realize that getting out of bed and showering is truly an accomplishment when you feel crappy. Celebrate the small victories. Its the first step that is always the hardest so focus on that rather than the whole task and it will be easier to get into the mode where you're ready to think about tackling exercise or whatever.
My thoughts are with you,