I'm sorry I could not keep track of all of your fish, did the newly added Corydoras die or the ones you already had? It does not matter whether fish are wild caught or farmed, quarantine them all for 4 weeks.
I am not a proponent of prophylactic treatments, improper use of medications (such as the one you are proposing, it is way too short) has led to "superbugs" in both human and veterinary medicine. It is normal for fish, as well as any other animal, to carry a range of microscopic pathogens. When fish get stressed due to whatever reason, their immune system gets impaired and pathogens can take over. Proper quarantine and water conditions should in most cases be sufficient.
I know most members here will disagree with this as they will say you not only need antibiotics but need to de-worm them as well cause they might have flukes and what not cause that is the 'big pharma' thing to do.