I think I might have a problem...But I'm afraid of telling my parents?

Before I begin, I would like to point out that I do NOT have an eating disorder! My mom took me to the doctors last week. The doctor said I need to gain some more weight (I'm 14 I'm 5'7 and I weigh 110 pounds). So I started working out at the gym to gain some muscle. But I admit that I haven't been ga owing the doctor's orders. They put me on a diet to help me gain weight, but I haven't been fallowing it. I lie to my dad and tell him that I am eating all the things I should eat. But I'm not really eating as much as I should. It's just that, I don't want to get fat. But I do eat, but I skip breakfast and lunch and then I try to eat less at dinner. But what makes me think I might have a problem, Is because I know I have to hide it from my parents. Its just that, I shouldn't have to hide anything if it isn't wrong. But I just can't get myself to eat it. I passed out at the gym today, because I didn't eat. I want to come clean and just tell them that I've been lieing, but I'm embarrassed. And I'm afraid of telling them because they will probably freak out on me and get mad. How do I tell them that I've been lieing, without them getting mad?