What is wrong with me?

Did something happen that made you feel this way? It can be "one big thing" that can cause you feel like this, but it can be lots and lots of small things such as being bullied at school or having an argument or loosing a friend, building up and causing you to feel like this. Whatever happened, you should know, that people do care, and there will always be people you can turn to and tell how you feel, and ask for advice. You should never feel like you're alone, because honey, you're not.
You shouldn't care about all those bullies, or those fake friends, that can only criticise you, and make you feel awful. You shouldn't care what everybody thinks. Because no matter what you do, you'll never please anyone. And sometimes whilst you try to please the people you hate and the people who put you down, you might loose the people who are there for you. You shouldn't go ahead and try to please everyone, because there is no way it's going work. You should just bother and care about the people, who return your support, and the people you know are going to be there when you feel upset, depressed or down. Because these people do care for you, and want to make you happy no matter what. These people might be your parents, your friends, your siblings. Doesn't really matter in what way you know them, but they are the ones worth staying strong for.
And Sweetheart, never try to deal with everything on your own, no matter how strong you think you are. You cannot deal with everything on your own, and you got people to help you get through the tough times. If you feel down, and feel like you cannot cope on your own any more, do not hesitate to tell your parents or someone you trust that you have problems you need help with. In your question, it seemed like you are very close to your parents and they are precious to you. I am sure they feel the same way about you, and will love and support you no matter what. So go ahead and tell them what's wrong. Tell them how you feel, or in fact you don't even have to say anything. You'll parents will be there for you even when you're upset for no reason and just feel like crying. They will give you a shoulder to cry on.
The longer you try go on, and cope with thing on your own, the harder it will be. The worse it will get. Just do whatever makes you happy. Be who ever you would like to be. Dress however you are comfortable. Listen to what you truly love, and not to what today's society expects you to listen to. Look up to, who you want to be when you grow up. But, never ever try to go against your happiness just to please someone you don't even like.
It'll get better, it always does, even if you don't realise it at the moment. But I promise you, that it'll get better, as soon as you give up trying to fit in with society.
I've been suffering from depression, and been self harming in all sorts ever since I was 8. I am 16 now. I tried to take away my life various times, thinking that I don't worth it, and that nobody cares. I never told anyone up until a 1 year ago. And it got better, Slowly, but it definitely got better. You're not the only one out there who feels like this, and is suffering of this. There are many of us out there, and those of us suffering, we can help each other. There will always people who went through thing similar that you went through, and there will be people in the future who will go through similar situations. And they will help you.
Lastly, please do not ever consider self harming, or taking away your life ever again. You are beautiful and unique. Whenever you feel down, please read this again and again, and realise that it will get better, you just got to find the right people that you can rely on.