What you might want to do in addition to or in placement of neosporin is to wash the wound with hydrogen peroxide (HP) then rinse with water...pat dry. It would need to be cleaned as described two to three times a day until the skin scabs over or when new skin covers the wound. Use the neosporin or what I prefer, terramyacin after cleansing and when the wound looks infected (swollen, red and irritated).
If signs of infection is absent, it is best to avoid antibiotics and just keep the wound clean. This helps prevent antibiotic-resistant bacteria from developing.
Being this bird was attacked by a dog, look for punctures. Injury may have gone further than the surface of the skin. In this case, I would advise against the use of an antibiotic ointment and stick with the HP treatment until the tissue under the skin heals, then go ahead and use antibotic ointment if signs of infection occurs, though should remain fairly clean if you keep up with the HP treamtment. If an antibiotic is needed for a wound deeper than the surface of the skin a veterinary visit may be in order.
You also may want to feel her body for any lumps under the skin. Teeth and nails may not always break the skin, yet still damage tissue and become abcessed.
Just to note:
I am not a fan of neosporin. Why? It does keep bad bacteria out, but it can also seal bad bacteria in, thus may actually slow the skin's mechanisms of renewing damaged tissue. This is something I found out at college in a biology class.
In my own experiences with treating animals of many different kinds, I have found terramyacin to be effective, yet gentle and gentle enough to be used on eyes if ever needed. It also seems highly recommended by many vets for skin sensitive animals (such as amphibians), so should be safe for a skin injury on a chicken.
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