Fungus on swordtail not going away

I posted this in the Newbie forum but didn't get much info so I thought I'd post it here .... I apologize if I shouldn't have double posted ... I'm just concerned about my sword >>>

I recently added a new female sword to give my male company. Within a day of adding it, I noticed a white fluffy thing growing on its tail. There is also a tiny fluffy patch on its top fin as well.

After reading up on previous posts, I decided to go with the Aquarium Pharmaceuticals' Melafix. I've treated the tank for 3 days now and have seen no improvement in the infection. It hasn't gotten worse though and none of the other fish are showing any signs of having it either.

Per the bottle instructions, I added 1 tsp. per 10 gallons in my tank. The lady at my LFS told me that this was one tonic that I COULD use with my filter media still in the filter. The media is a blue sponge-like thing with black granules in it (i'm guessing its carbon).

Could this carbon be causing the medicine to not work? If I do indeed need to remove it, the filter will be pretty much running without any media ... so the water will not be getting filtered at all. Is this something I need to do?

Oh and one more thing .... the infected sword hasn't been eating at all for the past 2 days.

Any suggestions would be greatly appreciated ... I am really lost and have no clue what to do ... I don't wanna lost the fish

Thanks for your input OrionGirl !! I was running on a sorta tight budget right now .... but I guess I should go out and get a tank to be used as a quarantine tank. Would a 5 gal serve the purpose?

Should I leave the quarantine tank empty without any gravel/decorations? Should I fill water from the established tank to get the new one going ?

Thanks again for your quick response !!

EDIT: Any particular brand name of broad spectrum antibiotic that you would suggest ??