My parents are putting me on a diet. I need an opinion?

I am a swimmer and have been all my life. I swim everyday for 2 hours, run, and lift, all while going to school as well. I competed in the Olympic Trials and other big meets. This past year has been a off year for me and I haven't done as well. My parents decided that I need to go on the Atkins diet. I am 5' 7 and weigh 135 and I am a girl. The Atkins diet says that for 2 weeks I can only have 20 carbs a day and I have no energy! Should I stick with the diet? Or tell my parents I can't do this.