Injured black skirt tetra with white, fluffy growth... should we quarantaine it?

Hey everyone! I am writing this post because we are very worried about one of our black skirt tetras. Five days ago, I found the fish wedged between the filter casing and the glass. I freed it immediately but noticed that it was injured. My housemates and I decided to minimize any stress but leave the fish in the community tank, as we have seen our first black skirt tetra act very stressed before the others were added. There are no agressive fish species in the community tank, just some cardinal tetras, zebra danios, naked rasboras and red cherry shrimp.

Now most of its injuries are healing nicely, but the largest one (see pictures) is very deep and we have noticed white, fluffy strands seeming to grow on or out of the wound. It was quite difficult to capture on camera but I hope that the pictures are clear enough.

Now, we are unsure what the right course of action is: should we place the fish in a quarantaine tank and treat it with salt or antibiotics? Is this a bacterial or fungal infection, or something else? And is it ethical to keep this fish alive or is it suffering a lot? It appears to act normally, and does not have trouble eating. We worry that placing it in a quarantaine tank will give it stress and thereby hinder the healing process.

I'd love to hear your advice and opinion on this problem. Thanks in advance!

I've looked through my phone and found images of the fish right after the injury occured and on day 3. If I look very carefully at the video I think that there was also some white, fluffy stuff on the wound on day 3.

I've been thinking about the options we have for quarantaining this fish. I have a small 4 gallon tank that has been running for about a year but has been empty (only gravel, heater and small filter) for two months now. I'm thinking if I give it a good clean it could be useful.

Would I need to add water from the big tank to reduce the difference in water composition? And could I soak our tacky purple plastic plant in boiling water to clean it and use it to provide the fish a place to hide?

I'm pretty sure that the white fluffy stuff is a common fungus. It is not unusual for it to grow on wounded areas.

If it were me, I'd quarantine the fish and treat it with an anti fungal for several days.

QT the fish. Do daily water changes if 70%. Also add 1/2 tablespoon of aquarium salt for every 5G of water you have him in. After first day, only add 1/4 tablespoon of aquarium salt after each 70% water change. Be sure salt is dissolved first before adding. Fungus grows faster in warmer water so lower his temp a bit. Do this for 10 days. The salt will also act as an astringent to keep the wound clean. Keep us posted on how he does.

White fluffy stuff on wounds is saprolegnia fungus that grows in damaged tissue.

Do as deanasue suggested, big daily water changes and salt for 2 weeks.

If there's no improvement after a few days of salt you will need a broad spectrum fish medication (not an anti-biotic) that treats fungus and bacteria.

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Don't expose plastics to heat because they leach chemicals into the water when heated up.

If you have a plastic plant that needs cleaning, hose it off or soak it in a bucket of bleach for 30 minutes, then rinse really well with tap water.