do you think this could be balemia?

Dealing with depression and a lot of stress can easily make someones appetite change. In your case it made you not hungry, which is extremely common.
My best guess is that your lack of appetite had just gone on long enough to make your stomach shrink, so therefore it would feel full much easier then before.
Also, 3 to 4 months of not really eating could have caused your body to automatically go into starvation mode. Basically, a switch in your mind turns on and convinces your body that you are starving, so your body then eats away at what it has, your fat and muscle.
This may be a really odd example, but people that were in concentration camps would never eat and the ones who survived and were free were starving...when they ate, their bodies could not handle it, and their stomachs exploded...(really depressing, I know)
I am not trying to use that to scare you or anything either =P I am just trying to better explain, that this is just how the body works.

You feel like throwing up, because you are being forced to eat more then what is comfortable for your stomach. So, you are not bulimic! When someone is bulimic they physically make themselves purge. The person is making a conscious decision to throw up, nothing else is causing this.
However, I would maybe try and get help for your depression and stress, because it sounds like it has clearly taken a toll on your body, and you don't want to let it get out of hand. I hope this helped you a little. If you have any questions I am always here to try and help figure them out =) hope to hear from you!