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.