A topical steroid cream with gentamicin is my "go to" for skin ailments. Looks a lot like the scratches that my horse gets, or ring worm, or rain rot, or whatever you want to call it. It's all the same thing, just on different parts of the body.
I get my gentamicin cream from my vet. It's water based and absorbs right into the skin, usually requires only a week of application before the active infection and fungus are controlled.
They say money doesn't buy happiness -- well happiness doesn't buy horses!