I feel for you in your situation - It is an exceptionally terrible predicament to be in. A few questions I must ask you - What is your relationship like with your father? How old are you? And also do you have any brothers or sisters?
Depression is a terrible illness and I do not deny the fact that your Mother must find her life difficult however it can be beaten! But it can only be beaten if your mother wants to beat it.
Your have turned from being her source of moral support into her servant.
Your Mother must realise that you are still young with the chance to grow and make something special with your life, obviously your decision to apply to Uni is your first step towards making a better life for yourself.
I am afraid that the time has come for you to be stern and determined - I believe that by standing still and allowing her to overcome & suppress you (i.e. Stop you from seeing your bf, cutting you off from your friends) will only make the situation worse. If you do not act then you may find that one day you will have turned into your Mother - Alone & Depressed.
Try talking to her and stating your feelings/concerns, if she does not listen (And it does sound like she will not) then you must decide what you are going to do. Do NOT let her stop you 4rm seeing your bf and/or friends anymore, go strengthen those relationships! Next time she books 2 weeks off work tell her that you dont mind hanging out with her for a little while but you have your own life as well. If you do hang out then tell her that you both should do something fun, e.g. shopping, cinema, ice skating whatever and STRESS that you will not stay in the house and mope with her.
If all this fails then perhaps you might consider seeking the support from your Dad & possible staying with him (This doesnt have to be 24/7 - perhaps a couple of days in the week) Tell him how you feel, how his arguments with her affect you and also how she makes you feel. He should support you.
You are in a terrible place, and I am not saying turn your back on her because she is your blood after all but at the end of the day you can't help someone who wont help themselves!!!
You must go to University if thats what you want to do and AGAIN STRENGTHEN your relationships with your friends, your boyfriend otherwise one day you may find that they have grown tired of waiting for you and you wont have anyone left.....Like you mother.
You only have one life - LIVE IT! And hopefully your Mother will see sense and follow your lead! It will be hard but no has ever said that life was easy.
Good Luck!!