Hey. You know, the most irritating thing about being a teenager is that our hormones are absolutely everywhere. Just as you said, one minute you feel grand and the next your whole world has come crashing down. I'm saying this just to let you know that, I promise you, you're not alone in these feelings, yeah? So many people your age are feeling like this and, although it sucks and is really really difficult to deal with, there are things you can do to deal with it effectively, ok? You mentioned that you cut yourself, and I think that in order to quit the cutting, you need to deal with the reasons behind the cutting, y'know? It sorta makes sense, don't you think? So, issue one that you mentioned, is your weight. A lot of people think they're fat, and it can really get you down, can't it? Quick question though - are you actually overweight, or do you reckon you're being a bit hard on yourself? If you are overweight, and you want to make some changes, then I don't think that's a bad idea at all. It'll make you a healthier person all round, which is important. However, I advise that you maybe pop along to your doctor and have a chat with them about this. What do you think? You see, if you ARE overweight, your doctor can help you work out a new diet and exercise plan. Think of it as a new lifestyle, a lifestyle that's gonna make you a healthier person. Thing is, you only need to do this if you want to change and if you need to change your weight. As I said, a visit to the doctor should clear this up for you.
Even if you aren't overweight, it definitely sounds like you're having some self-esteem problems, especially as you're calling yourself fat. 100, 200 or 300lbs, you need to learn to love you for who you are, imperfections and all. A huge amount of people struggle with self esteem problems, but it'd probably do you the world of good to build up and work on your self esteem. This quote here makes it quite clear what self esteem is and why it's a good thing to have!
Self-esteem means 'appreciating your own worth and importance' - and it helps you to cope better with the challenges of life. 
- Tracy Turner
Positive thinking is definitely a must. Give yourself compliments, think about all the great and wonderful things going on in your life, think about what your plans are for the future, think about what you like about yourself. Think about these things often, hmm? Remember that you deserve happiness and good things and that you are a good person.
This website is really, really good with tips on how to build up your self esteem, so perhaps have a good read through it, hmm?
http://www.netdoctor.co.uk/sex_relationships/facts/selfesteem.htm
Your shyness is also something that you can work on. Shyness really is horrible, isn't it? It's ok to be a naturally quiet person, but if you feel like you want to get out there and do things without your shyness getting in the way, then definitely have a think about actively doing something about it. What I find really effective is faking it! If you're not a naturally confident person, then pretend you are! That sounds a bit weird, really, but it's not as hard as it sounds. Smiling is a big factor. Someone who smiles a lot will seem like a naturally happy and confident person, and it'll attract people - it'll make you look approachable. You mentioned that you don't do anything, so you can actually combine building up your confidence with doing things. Maybe have a think about joining some clubs and taking part in some social activities. This way, you'll be forced to meet new people and interact and you'll be busy doing things so you're not left alone to fret about it all, hmm? This website has some good tips on how to build up your confidence:
http://www.mindtools.com/selfconf.html
I think it's really so very important that you keep yourself busy. Get out and about, do things. The more you sit at home then the worse all your problems will seem.
And the cutting. The cutting really is a big problem. You must be really hurting to do that to yourself, hmm? How you would you feel about talking about how you're feeling? Do you have anyone around you who you'd think would listen to you? A parent, school counselor, teacher, friends? Anyone at all? See, I think it's really important that you get all this stuff out and talk about it. Hiding it isn't going to do you any good in the long run, so I honestly think it'd do you the world of good to find someone to talk to about all of this. You don't have to tell them about the cutting if you don't want to, but you could at least give talking about how bad you're feeling now a go, hmm? Think about it.
My inbox is always open to you if you ever need a chat. Take care of yourself.