Not quite as strong as penicillin, no. But it does have antifungal/antibacterial properties. Both Melafix and Pimafix should be readily available at any LFS.
Keeping the water agitated is a good idea, but the problem is that you don't have any beneficial bacteria in the hospital tank since it was never cycled. What kind of filter do you have on the 55g? If you have filter media that you could remove (filter floss, sponges, other biomedia) then I would consider buying a cheapo power filter for your hospital tank and sticking some of the filter media from your 55g in it. Until you do this, you'll need to do large water changes on the hospital tank every day to keep ammonia levels from building up. Water changes in a hospital tank are a bad thing, since every time you do one you're removing medication from the water that you have to add back. So, you see why it's important to have a cycled filter running on your hospital tank.
In the future, you can keep this cheapo filter running on your 55g next to your main filter. This way, the filter will always be stocked full of beneficial bacteria. If one of your fish gets sick, fill the hospital tank, throw on the extra filter, and bam, you've got an instant-cycled hospital tank ready to go.