I have pain in my left mid/lower back after eating certain foods (fats?) the pain is constant and dull and lasts for days. What could be the cause?

Not sure. It is unlikely related to the food. Do you sleep well or grind your teeth at night; if not sleeping well the muscles dont relax to allow blood flow in to heal a potential site of inflammation, this can cause a recurrent circuit that makes back pain easier to get. Mood can play a role, insomnia is a psychiatric "vital sign", use 2 aleve (naproxen) bid but can't think of a food assocaition, may get better answe.