If you do, it's something other than anorexia or bulimia. But I don't really think loss of appetite due to depression is considered an eating disorder though. But try not to focus on the labeling. When you talk to your doctor, repeat the specifics of your problem and let him know what you want to eat, that your relationship with food is fine, but your loss of appetite is from your depression. You should get treated for your depression and see if that helps. There could also be other things that are preventing you from gaining weight other than metabolism, so just make sure it's not something else.

I don't know how much you weigh but there is a certain point where you should be hospitalized if your bmi is low enough. I've seen people with bmi of 14 and 15 and they are running around in good health and vitals, which seems dangerously low but isn't always the case.

Red flags that you might be too low of a weight is, dizziness, fatigue, bloated belly, period irregularity. It's more about how you feel than how you look.