This is an interesting reaction and you should be congratulated for listening to your body. Truthfully, I have no idea, but I offer the following:
Is it allergy, detox reaction, or improper metabolism?
Do you have any reaction to the other oils, Vit A or E, or do you take them separately. I think you need to find out if it is just the Vitamin D, or others. Cod liver oil for example has both A and D.
Do you have any other symptoms that would say that the Depression is a detox reaction, for example headache, nausea, etc. Do you get Depression if you drink Vitamin D milk? Or symptoms of improper fat metabolism, like gas, bloating, or diarrhea?
If it is an allergy, could you not find out by taking tri salts or Alka Seltzer Gold to determine that?
I am really interested in this because years ago I had a severe fat metabolism problem. My family cooked in bacon grease, and when adult, I ended up with Gallstones when I tried to go off all fat and oils because it gave me such gas, bloating and diarrhea. If I would eat bacon and eggs, I would have to go right to the bathroom. During this time, my stools were never formed, but I thought because I had so much gas and bloating, the cereal I ate was the proof of "enough fiber."
I have come a long way since then, and I am not sure what one thing attributed to my success. I took L-Glutamine for a long time and swore off raw foods to let my intestines heal up. I found out what real fiber was, and I feel my intestines are in pretty good shape. That is, until I read your post, and it reminded me that I have a smaller reaction than before, but still a reaction to heated fats and oils. I use only healthy oils, but I had noticed it and decided to ignore it. Even coconut milk affects me and I always add it at the last minute. I don't have the reaction to fish oil capsules or Vitamin A, D, or E capsules (that I connected anyway).
So if anyone comes up with ideas, I want to find out too. I do hope someone with experience comes forward with at least a clue.