Strange, Whip-like Worms In Goldfish Tank

[RandomWiktor]

My goldfish have been fighting horribly recently, so I figured their missing scales and lip wounds were from attacking one another. I loaded the tank with (fake) plants so they couldn't build up the momentum to fight, but I was still finding scrapes and missing scales. So, I started watching carefully, and realized they were both darting and flicking a lot, sometimes to the point where they whacked and scraped their noses on the gravel and ornaments. I bought Jungle Parasite Clear (would love to use General Cure but its a tad pricey for me) and decided to do a significant water change (as they were due) then start treatment.
Well, as I was cleaning, I was shocked by what I found amongst the fecal waste - small, whip-like worms, ranging in color from off-white to reddish-brown. They were completely smooth and tapered on both ends, approx. 1cm long but very narrow. They did not have frilly "heads" on one end like blood worms, and were on the plastic plants and in the gravel wherever there was fecal waste.
Do my goldfish have intestinal parasites so heavily that they're pooping them out? Or is this something else? Could it have been introduced to the tank by pellets, krill, or fresh greens? Should I be deeply concerned about my goldfishs' health, or will the Parasite Clear take care of this?
Thanks.

 

[WILDER]

Do they have a forked tail the worm as anchor worm can look like nylon with a forked tail, check the anus of the fish to see if they look inflamed or larger than normal.

Look at anchor worm first to rule it out.
http/www.2cah.com/pandora/Disease.html#Lernea

http/www.skepticalaquarist.com/docs/health/nematodes.shtml

Look under anchor worm.
http/www.fish-disease.net/diseases.htm

 

[RandomWiktor]

Hmm... no forked tails, and the fish haven't had any on them. Anuses look perfectly fine, no redness, swelling, or distension. I haven't seen worms on the fish at all, and I watch them very carefully. They do have some injuries around the mouth that could be considered ulcer-like, but I saw one of these injuries occur, and it was from panicking and running into the cave in the tank when he spooked, so I'm thinking they're more related to injury than illness.
I am using anti-parasite fizz tabs either way; they kill invertebrates, so even if the worms are non-parasitic, it should take care of them, right? Being feeder goldfish, I'm sure they probably have SOMETHING, especially with the flicking, since they come from pretty lousy sources. The last time they had an anti-parasitic done was when they were just babies, so I'm guessing its time again.

 

[WILDER]

If water quality is good and they are flicking it does sound like a parasite, parasites can cause ulcers, look on the body for pierce marks puncture wounds, sometimes they will look red and a bit swollen.