Will this help me lose weight?

Heres the deal, I am 16 years old and i weigh about 123 lbs. Summer is coming up and i know im not fat, but im not skinny. I feel so uncomfortable with the way i look that i never wear shorts ever and i rarely wear skirts. I just want to get thinner so i can wear shorts like everyone else and be comfortable by june. I am willing to do whatever it takes because i am over feeling fat and ugly. Right now my plan is to have a very restrictive diet. This means i would only eat 1-2 apples and maybe a couple bites of a lean protein such as chicken breast a day. In addition, I am planning on going to the gym at least 4 times a week for over an hour where i would run and bike. Will this make me lose weight quickly?