You should be doing more frequent water changes than every 3 or 4 months. You need them for more than just controlling nitrate. They are also needed for controlling phosphate, replenishing KH and other essential mineral, removing harmful organisms. There will be all sorts of imbalances in your aquarium, and the end result is things like algae growth.
While zero water change aquariums are a thing, you need to other things instead. Very low amounts of fish, heavily planted with high nutrient demand plants, dosing essential minerals etc.
I would be very suspicious of nitrate readings of 15ppm after 3 or 4 months regardless. You dont have many fish, but you also don't have a lot of plants. I would expect it to get to 15ppm in 1 or 2 weeks. What test kit are you using? I would get 2nd opinion on your water testing, and get into a much more frequent water change routine. 50% twice a week until your algae is under control, and at least 30% a week, or 50% every 2 weeks going forward.