Janet,
Three weeks is a little early for the cycle to have completed, so I would suspect part of the problem is new pond syndrome. Stress of too much ammonia. Have you checked the KH, as a stable pH would help both the filter and the fish. I would not be putting antibiotics in the pond as they kill bacteria, good and bad, making the cycle go much longer. If the KH is over 100ppm, then I would be suspecting parasites, which become problematic with fish that are stressed and the cycle is definitely stressful. Low KH would cause pH swings which are stressful.
Assuming it is parasites, I would be looking for a product that has formalin and malachite green, which you may or may not have there. Don't know. But the fish/aquarium stores should be able to recommend products for ich and flukes. The use of high dose salt could be useful except that you want to keep the plants and they would not survive 0.6% (5 pounds per 100 gallons) salinity that I would recommend for most parasites, but for ich, it would have to stay in the pond for a couple of weeks.
Zone 7 A/B
Keep your words sweet. You never know when you may have to eat them.
Richard