My betta fish's fins have become shredded and pale over the past few months, and lately…

My betta fish's fins have become shredded and pale over the past few months, and lately, he has been lying on the bottom of the tank a lot. I’ve tried water changes every three days, putting in the almond leaf, aquarium salt, and taking out the plants. He lives in a five and a half gallon tank, has a high quality filter, and a water heater. I got him last October in very bad condition for free (because they were going to euthanize him,) and he improved for a while, but now he seems sick again. He is still eating, but he seems to be in very bad condition. The water looks murky because of the Indian Almond leaf. I wanted to know if I need to get him on antibiotics, and if so, what type. Any and all advice would be very much appreciated.