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Hello. Thank you for asking your question on just answer. My name isXXXXX will try to help.
Yes neosporin is fine. It is not toxic if she gets some on her paw and licks it.
You can apply it 3-4 times a day as needed.
It may also help to put an elizabethan plastic cone on her so she will not scratch the wound as it heals. It will itch as it heals. You can by an elizabethan collar at any larger pet store like pet smart.
You can also apply hydrocortisone cream to the wound twice a day, to help with inflammation and itching, as needed. That is not toxic either if ingested.
I hope this helps.
If there is any debris in the ear, or the ear appears red or inflamed, then "yes" because she may have an ear infection.
Also, the spot behind her ear may be infected, so antibiotics may help the wound heal a lot faster. Signs of infection are moist drainage, yellow drainage, a bad odor, red inflamed skin, and heat around the wound.
It does not sound like an emergency.
I would start the home treatment today.
If it is not greatly improved in 48 hours, then take her into the vet.
If the ear is not infected, the vet may not be able to tell you how the wound got there.
There is always bacteria present on the skin. Anytime there is a break in the skin, the bacteria can enter the skin and cause an infection. It could have been from a scratch or a bug bite.