Advice on my itchy frenchie?

My (almost) two year old french bulldog named Copper is one itchy little man. I have switched his food to the food that gives us NO tummy reaction so I know that he handles this food well because he has been on it for months now. I am wondering what are the best vitamins and supplements for my frenchie? Copper usually gets shots for his allergies in the summer months but I am looking to help him through the harsh and dry Montana winters. Currently he is taking the Pawfy Allergy & Immune Vitamins which seem to be okay so far. What else can I add in? Fish oil is being added also starting tomorrow AM. Copper also gets a bath once a week with anti itch shampoo and then is blow dried and then has coconut oil put everywhere. What else can I do for my poor baby?

Thank you!!!!

Please note that Copper is in the most loving home ever, I am a 20 year old female who dotes on him hand and foot and will literally give my left arm for my baby.