It sounds like a bacterial infection from poor water quality; most of these kinds of things in goldifsh are.
Please don't feel as if I'm having a go or anything, but I do feel I have to be honest with you.
Your tank is severly overstocked, I'm afraid. Fancy goldfish need 20 gallons each, and long-bodied goldfish don't belong in tanks at all; they need to be in a pond.
In all honesty, you need to either get a bigger tank ASAP, or re-home these fish, because they can't stay where they are for too much longer.
When you changed the filter, did you put any of the media (that's sponges or something) into the new filter? If you didn't, you will have lost any good bacteria, and there will be ammonia building up in the water.
While you're thinking what to do, do daily 50% water changes, with dechlorinated water and cut the feeding right back.
This will (hopefully) help keep the fish healthy for the next few days.
Try not to panic; we've had worse problems than yours here, and you're in the right place to get help
Post back if you have aany more problems or have any questions and someone will get back to you.
Good luck