I honestly don't know. Was hoping someone else would chime in that has more experience. I've only been back in the hobby a year and have never used medications other than anti-parasite food.
As far as I know, to medicate you need to know if it's bacterial, fungal, or parasitic. The hole could have started from another fish biting it, then it could have become infected, which I believe usually starts with bacteria but can develop fungus if left untreated. Or it could have started from a parasite and then became infected. I'm not sure what it could be or how you would treat it. You may need to treat a few different things at this point, but some things you can't treat together or the medications could react to each other.
This is only IMO and I cannot say whether or not any is fact.
You say you don't have a QT tank, but do you have an empty bucket perhaps? That could work. Just add an airstone, heater, and sponge filter and change a significant amount of water each day. Sponge filters are easy and cheap to make for such a small amount of water and most pet stores sell small, cheap heaters. If none of your other fish have been affected after this long, it probably isn't a parasite but instead started as an injury. If other fish are showing any symptoms of illness, it may be a parasite and you'd want to treat the entire tank and wouldn't necessarily need to QT the one fish.
Do some research online to see if it looks like a bacterial or fungal infection. Sorry I can't be of much help.