A hurt bird is traditionally read as a wounded hope or a sensitive part of you that needs gentleness. Caring for it in the dream is seen as willingness to heal something slowly.
Does the traditional reading fit your dream, or did it mean something else to you?
My Cosmic Code has a private dream journal. Write a dream down and the app picks out the symbols in it, shows what dream books say about them and, over time, which words recur across your entries. The journal is stored on your device only.