|Are injections the only real cure for mouth rot?
Well, if the fish were valuable and the stakes were high for a successful outcome, I'd say injections would be the best way to go but NOT by any means the only way to go.
Medicated food is a good choice, even IF you chose to inject the fish. Dressing their mouths with an ointment or hydrogen peroxide is also commmendable, ONCE. Do not over dress a wound or you will conversely inhibit healing.
Baths for several hours a day in Furazone Green can go a long way to healing the fish as long as the baths are large enough. People put large Koi in tiny tubs only to have them harm themselves in the tiny boxes. Rubbing their mouths EVEN MORE in small quarantines is worse than no facilities at all.
If I had a fish with mouth rot that mattered to me I would inject it once. I would swab its mouth with hydrogen peroxide making SURE that I did not get peroxide down the gullet on the gills. I would then offer medicated food and make SURE that my water tests always showed "perfect water" and if the fish did not improve in a few days I would re-inect and seriously consider warming the fish in a soft, rubber sided holding vat in my garage.