There are fatty acids in almost every foods. Fruit has more than people think. You can still eat plant fats such as nuts, seeds, olives, avocado, just don't have more than about a palm-full per day.
I recommend ditching all oils. No where in nature are oils found naturally. They are all a processed food. All this push for more Omega 3's in the last decade is to try to offset everyone's super high intake of Omega 6's from things like olive oil, which was never high in the Mediterranean diet btw...
Why can't you eat fruit? There also seems to be a correlation between sickness and low fruit consumption. I was one of them. Now I'm eating around 10 pieces of fruit per day.