About two months ago my mom brought home four goldfish from the hotel she works at. Long story short, they decided to have goldfish as a banquet centerpiece but provided no proper water treatment and were handled very wrongly.
Three died that night even after they were carefully tended to, from what, after some studying, I learned were infected wounds. The survivor looked healthy enough, apart from a very tiny wound by the base of his tail, (where the dorsal fin ends).
I knew very little about fish then, and thought it would just get better itself since it was so small. The day after I went to a pet store and got a half gallon fish bowl. I later learned that this won’t be good for long, but at present it’s better than a vase and we can’t afford anything bigger.
By a month later the wound was very much larger and red, with a bit of puffy white around it. I was recommended to an enzyme fortified aquarium salt. I at first changed half of the water every day, adding the right amount of salt each day.
Now you can barely see any red at all, but there’s a pea sized clump of white fluff on the skin. It doesn’t affect the fish’s movement or behavior, but it worries me. I now clean the whole bowl and gravel once a week more or less, and still add the salt. Of course I have water treatment as well.
Now to the real question: how can I treat the wound? I’ve heard that tea tree oil can help. I want to spend as little money as possible, and have these things at home:

100% Alcohol
70% Isopropyl Alcohol
Tea Tree Essential Oil
Aquarium Salt

I was wondering if there’s anything out of that that I could use to treat it, and how I would do so. If the above is not useable, what could I use? Is there anything else I can do to help my fish?

Don’t say she’s going to die. She’s not, and that’s just plain rude. I’ve already got almost enough for a larger fish bowl. Leading me to another question: what size of fish bowl should I get?

Please remember that this is a half inch long feeder goldfish, nothing fancy.

Thanks guys!
Thanks for your replies so far! I’m definitely saving up for a filter, and may try a very quick salt dip. I’ll also put the alcohol and oil away. xD I didn’t think it could be useful, but just wanted to put it out there incase.

I had a question about the swabbing thing. I’m not sure how I would swab the little guy, exactly. He’s so tiny and I don’t want to stress him out too much.

I also realized that I have a tank buried in my closet from when I had walking sticks. The bugs. I’m not sure if it’s 10gallon or 20 gallon, but I think I’ll clean it out and set it up. Any tips on that? I’m not sure what cleaning stuff is okay to use on it.

Feel free to post more answers, I’d love to hear more. Thanks for any links you provide. :]
I’ve set up the 10 gallon tank, put gravel at the bottom, installed a cheap-ish in-tank filter, and put the fish in after letting the filter run for a few days.

I was already using water treatment, I’m not that dumb when it comes to fish.

I’ve given the fish two salt dips, which cleans off the fungus, and have been doing what the Melafix bottle tells me to. She seems to be doing better. Is there anything else I should do?