If you're sure about the dropsy, it may be a lost cause. I don't think the air-breathing is going to stretch things out as far as cold, alcohol, or clove oil is concerned.
There are some topical treatments for fin rot including, Google tells me, gentian violet. It has some fairly personal uses for humans so a pharmacy may have it if your LFS doesn't. I would look into a fin rot specific topical treatment.
You should also be aware that penicillin isn't always the best antibiotic (leaving aside the question of whether or not we should give antibiotics to fish). Gram-negative bacteria are apparently inherently resistant to penicillin. At least one genus of fin rot causing bacteria (Aeromonas) is gram negative. Another, Pseudomonas (also gram negative), "is resistant to Penicillin, tatracycline, erythromyacin; sensitive to cyproflexin and genomyacin".
I'd try to find something that'll work specifically against gram negative bacteria or that is specifically cited as an appropriate treatment for fin rot.
Not to start the whole "do fish feel pain" war up again, but the best I can do at a fairly neutral rendition of what science has to say is that if they do, its in a fairly primitive way and that—completely lacking anything we might describe as a conciousness—they aren't particularly aware of it. The idea that they're suffering in a way that'd be similar to what happens to us doesn't seem to be the case.
If you decide you have to euthanize, rapid cold, clove oil, or alcohol all work rapidly and are humane options.