Just a few questions to try to help a little more:
- What kind of fish is it that is injured?
- What kind of fish caused the injury?
- What other fish are in the aquarium?
Most injuries will heal themselves without any effort on your part. If the injuries are serious (and it sounds like they are) the first thing you need to do is isolate the fish (which you have). The bucket with an airstone is probably not going to be adequate. You want the fish in an aquarium with filtration. The unfiltered bucket will foul quickly and the injuries may become infected.
Once the fish is in a suitable tank you can add some tetracycline and chloromycetin to prevent infection. You can find these antibiotics at the local fish store or chain.
If your fish can handle it (you didn't say what type of cichlid it is), you can lower the tanks pH level. A pH of 6.4-6.6 would be best. To minimize stress on the fish lower the pH slowly. Dropping the pH quickly can cause the fish more problems.
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Hopefully this helps. Please post some pictures when you get a chance. Good luck...