fish oil has omega 3 fatty acids, the omegas are what help with depression and mood disorders. there are other vegan sources of omegas (flax oil, walnuts, pumpkin seeds, spinach etc) and also the source that the fish get it from, algae. the reason your doctor probably told you fish oil was best has to do with how our body converts and absorbs the other forms of omegas. general health and diet can sometimes determine how well you convert and use omegas.
there are some negative points about omegas from fish (other than it being non-veg) that have to do with heavy metal pollutants. it is not currently recommended to take as mush fish oil as possible, in fact it is becoming more common advise on limiting fish consumption do to the fact of pollutants are present in the environments the animals lived or were farmed (fish farming is another negative). the supplements are concentrated which increases the percentage of pollutants.