Is it a good idea or a bad idea for someone who weights 110pounds to go into an eating disorder program when they should be weighing 115pounds?

My 8th grade of middleschool, I weight 100pounds. During the summer between 8th grade and 9th grade I ate a tub of ice cream and gained 15pounds. Scared about my gain, I started to eat less and work out more. Waking up at 6am each and every morning to go to school and work out. Than I went to working out for 15mins after I had gotten up from bed and before going to bed each and every morning and night. Than I started hola hooping for two hours straight. I lost weight. My mother started to worry and she had sent me to our work place were there is a nutrionist and I had worked with her for a few months before I continued to loss weight. My mother freaked out when I was trying on my clothes for the upcoming trip to Flordia for my 21st birthday and my mother had stop me from going to she the nutrionist and sent me to the hospital. There I was told that I either follow their meal plan or I will be placed into their inpatient program. Not want to go into the inpatient program, I worked hard to stay out of the intpatient program and it has been working great for a year now but I fear that I am slipping and I am going back to the ways that I use to be. I would agree that I wouldn't need to really go into an eating disorder program for I am only five pounds underweight but than again I have this idea that I can only be 115pounds and nothing more and that is a bad thought that I need to fix so maybe this whole eating disorder program will help me to gain alittle bit more weight than I would like to(that is scary)and than I will be able to move out finally from my thoughts and feelings of my eating disorder. Thank you so much for the help and thank you so much for your reply. You had really helped me.