Talk to your vet, there may be a pill he could take instead of the shots. It definitely sounds like allergies.

My cat had a similar problem. When the weather turns warm for summer his skin gets itchy. I think it is some kind of seasonal allergy or maybe he's just sensitive to certain foods. I was told by a very experienced cat owner that cats are often allergic to fish and that I should try eliminating fish from his diet. Also, I was feeding him something with a duck ingredient and for whatever reason I thought that might be contributing to his allergy as well so I eliminated that too. Voila! My kitty is no longer itchy and tearing at his fur. So I would definitely recommend a diet change. I tried Innova, which worked for my guy, but you may need to experiment with various brands before you find the right one for yours.

People get dry itchy skin in winter because of the lack of humidity. It's exacerbated by forced air heating. Some cats get dry and itchy too. Baths would actually make dry skin worse, not better. A whole house humidifier would help everyone. It also helps to minimize wood contraction in winter--you know, those gaps in molding and floors.