I cannot lose weight

I am a 49 year old female. Over the past 2 years I have put on 20+ lbs, I do not eat, I do not snack. I might have 1 - 2 meals a week. Otherwise I might have oatmeal, yogurt or a little fruit through out the day. I exercise about 45 minutes daily. My calorie intake is very low, maybe 600 daily.  My thyroid is good, I have blood work done twice a year and everything is "normal".
I am afraid to eat in fear of gaing more weight. I know your metabolism slows down if your not eating, but would'nt I lose weight if I'm not consuming the recommended daily calories? Something is wrong, and doctors don't seem concerned about this. What is wrong with me? Help!
Thank you in advance.

[Renee Radenberg]

You are eating not enough for your body and when that happens the body 'preserves' what it has. Metabolism does slow down, however, without enough food the body will start to break down protein and water will increase in the body. Suggest a measuring tape and not a scale. As you exercise you build lean muscle which weights more than fat. You may not see weight go down, however, your clothes size will go down. Suggest you start eating 5-6 small meals a day at 100-1200 calories per day so your body has all the nutrients it needs to be healthy.