The way you confront these types of fears, is through Cognitive Behavior Therapy, and that too would require you to visit a doctor. The general concept is that you conquer your fears by facing them, one small step at a time. But that's the truth of your situation. You're never going to get over your fear of showing your breasts to people, by never showing your breasts to people. In fact, that's how your make your insecurity worse.
The other person suggested that you might try anxiety medication, but frankly I don't think there's a quick solution here.
The vast majority of the population isn't Hollywood-attractive, and has multiple body parts they're insecure about. You aren't special or unique. Whether it be a small penis, saggy boobs, a fat tummy, being to skinny, being too hairy, no butt, a big butt, no legs, fat legs, fat arms, ugly facial features, poor intellectual capabilities, etc. You just need to understand that you're not alone, and that 90% of the people your doctor are "just as bad, if not worse" than you are. She doesn't care, you'll be out of her office in 15 minutes, and you'll insecure for the rest of the day, until you wake up the next day and realize it doesn't matter, and nobody cares (besides you).