If the nitrates are high, your tank is probably crowded, koi are in general NOT meant to live in aquariums. Mainly because they grow too big. So if you could give away the koi, it would help plenty!
Now, you should add medicine, absolutely! And if possible, it would be great if you could separate the bigger comet so he can recover in peace without the other one nibbling him
So, before you add the medicine, change some water, and use some of it in the quarantine tank. While you're treating the fish, you have to observe them. Are they eating well? Are they getting better or worse?
You should also monitor the water quality, because that will help their recovery. Change the water whenever needed, and add medication and water conditioner in proper doses for the replacement water