Fin rot, kanamycin doesn't help

[dendro982]

Hello, need help:
New baby fish developed fin rot in 2 days. Fast progress, in 3 hours was visible difference.

Both babies of the same kind - tassled filefish - were affected, while other same day purchase (lionfish) doesn't show signs of disease.

Started treatment by KanaPlex (Seachem's kanamycin). Dose should be given once in 2 days, maximum 3 doses. It significantly slowed rot development in the first day, but on the 3rd day of kanamycin rot accelerated again.

Here is photos at the moment. Dorsal and lateral fins are also affected. Pardon the quality, this is point and shoot camera and fish is constantly changing position.

http://i53.photobucket.com/albums/g78/dendro982/Fish/Dec03_08fin2222.jpg
http://i53.photobucket.com/albums/g78/dendro982/Fish/Dec03_08fin2.jpg
http://i53.photobucket.com/albums/g78/dendro982/Fish/Dec03_08fin4.jpg
http://i53.photobucket.com/albums/g78/dendro982/Fish/Dec01_08fin1.jpg

What can be added during dosing kanamycin (3 more days)? What next?

If possible, not killing biofiltration in one day. I have cycled sponge and ceramic media in sump or another tank, but not enough to replace all biomedia (LR, actually) every day.

My possible course of action?

[dendro982]

A little better now - yesterday added Nitrofurazone to Kanamycine, within few hrs white thick pieces disappeared.
Will see how it will be later.