Do I have an eating disorder?

I'm 14 years old, 5ft4 and 107lbs. My weight constantly goes up and down but usually I am around this. I often skip meals because I always feel extremely fat and disappointed with my weight. I work out everyday to try and tone my stomach and avoid eating whenever possible. I have tried purging but it hurt too much and I couldn't throw up so I gave up. Also I've also done the "chew and spit" diet before. My friends always say I'm skinny but I aim to be skinnier! I've lost a lot of weight within the past few months, help?