I use tea tree oil to treat anything wrong with the skin under the feather (or mane and tail) as well as other problems.
It knocks out the start of scratches in a couple of days.
For just treatment of the hair I just keep the dirt combed out on an as needed basis and while tea tree oil is also good for the hair I use coconut oil 3 or 4 times a year (it cost even less than the tea tree oil and does a lovely job with the hair, but won't help with skin issues)
We've never bought equine products to treat problems. Over priced and don't do any better job than the things we could pick up at the drug or grocery store. I can remember in my youth during warm/hot weather if an animal suffered an open wound injury my grandfather would clean it out, treat the severity of the injury and then coat it with burnt oil that had been drained out of a crank case. Kept the flies and bugs out of it and didn't need to badage it. It's amazing how people managed to keep healthy horses and mules that lived 30+ years without all the "equine" items that the market is flooded with today.
Off the topic.
One lady who knows me told me that for fun money when I retire I should package the vinegar solution I use to prevent thrush and sell it as a "Thrush Preventative" (it's nothing but 2 parts vinegar to 1 part water) and make a mixture with primarily tea tree oil and using different packaging so I can sell it for different things (thrush treatment, scratches treatment, etc....) I could even claim it may improve hair growth (it doesn't, but it will make combing easier so that fewer hairs are pulled out or broken and will treat most skin coditions that might be present). As she put it "just sell something as a 'horse treatment' product and people will buy it and pay more for it".