I’ve heard Neosporin works as long as it has no painkiller added. We have also gotten small antibiotic creams from the vet, I can’t recall the name at the moment.
Hi. IMO, you could try chamomile tea (standard commercial tea bags from the grocery store, which are generally German - not English - and have no additives), brew it with water, cool the liquid, and dab it one the scratch multiple times a day. The tea has both soothing and healing properties.
Neosporin works great. Just make sure the wound is not getting red and there his not a lot of discharge (a little bit of clear discharge that goes on to scab is fine).
The more important thing is why does the cat have that sore? Is it just a single abrasion or one of many? Is her ear itchy? Look inside the ear for discharge and all over the cat fo fleas. You get the idea...
And welcome to The Cat Site. Please come back and let us know what it turns out to be.