Listerine has alcohol which can dry, apply cider vinegar helps in fungus but some can be sensitive, coconut oil can be good but too much can irritate the issue. Flax is good for skin but you want to make sure it’s a stabilized flax or it will lose some of it beneficial effectiveness in storage.
If it is not an allergy which I recommend you check with your vet it may be an imbalance in skin ph.
I have uses pure tea tree oil in the past for skin itching. You can dilute it in a carrier oil but I Wld not get it predicted as some of the carrier oils irritate. Pure tea tree does not sting at all. Another product I have tried Ina clean rinsed mane is parnevu
It an herbal t-tree grow treatment for ethnic women. A little goes a long way. But it helped with any dry, itchy, red, Rashi, irritated, skin. It also helped with breakage and smooth down the hair. I also put it in my horses tail as he would scratch it on a fence post and rub it off, Even though he had been tested and treated for worms. I did not use it every day, I only used it once a week or every three days after rinsing off after a ride. But I do not show every weekend. It’s rather inexpensive and worth a try. Good luck keep us posted on what you you find out.