I hate myself

So I'm 17, almost 18, I weigh somewhere between 110 pounds and 115 pounds. I have a small frame and all my life have been told that I'm petite and tiny. But I don't feel that way about myself. When I look in the mirror I see a fat girl and I haven't been comfortable with my body ever. In my freshman year of high school I ate very little and ran a lot. In that year I lost 15 pounds. Since then I have lost another 10 pounds. I gained some muscle but this summer it's too hot to run and I had surgery, meaning I couldn't exercise for 2 weeks afterwards. I feel like I'm putting on weight even though my scale says I weigh 111 pounds. Working out has always made me depressed but now I just feel horrible when I do it. How do I not hate me? How do I find the ambition to lose weight again and get back my muscle?