water parameters? Size of tank?

The frayed/ragged/chewed-like tail could be the beginnings of fin rot. Changing water often can stop this and clean water allows things to heal naturally. As your goldies are growing over these years, it's possible they're outgrowing their tank? Thus water changes need to be increased and/or larger tank required.

With my fancy goldfish, I tend to veer away from chemical meds and increase salt (pond/aquarium salt) in the water.

I agree salt and a good water change are the best your fish look good. Maybe someone is nipping or they have snagged themselves on the hard looking coral with all those edges. I would do a good water change and take a water sample to the pet store they will do a free test. also add aquarium salt. let them go four days without food do not feed or care for them for the time you are gone just let them heal in the salt water. They will survive.

LOL...the coral does look real, doesn't it?
Actually...it's the backdrop/paper...âº
Although.....the damage could have come from the one artificial plant I have in there...(they're so ugly and have rough edges!)
The smaller one actually chases and nudges the bigger one around the tank.

I have well water with a water softener that uses salt as the filter medium...wouldn't that be enough salt or need I add it.

About them out-growing their tank...Gussie, who's about 7" long makes me believe you're right. He's/She's grown so big so fast! Fussy's still small...about 5 inches in length.
Thanks for the advice...will do a water change twice a week from now on, I reckon.

After doing some research online, I found this photo from another site. They call it a 'blister'...but what would it be from?
{{gwi:377785}}
Here's my poor fish's 'blister'...which is now gone, but it appears he has tail rot.
{{gwi:377787}}

I'm not sure specifically about the blister and its causes, but poor water conditions can do all sorts of damage - great and small.

What are your water parameters? What sized tank?

Water changes will definitely help to heal finrot, but pond/aquarium salt is also helpful.

Thanks Skygee...I've been doing the salt-thing for 3 water changes now.
It's only been a couple of weeks...the 'every-3-days' water changes alone haven't seemed to make a difference on Fussy's tail, so with the addition of salt teatments, I'm hoping he'll heal.