I'm wondering what you're feeding? Corn is big allergen for dogs, and can have a variety of ways it shows up.
Is he overweight - or is he just bigger? If he is overweight what are you doing to get his weight under control?
The shampoo sounds like a good start. You could use it several times a week to help him. There are also products that can be used after shampoo or just when they are wet to help with the itchiness - they aren't conditioners, but look similar
Hylyt EFA Creme Rinse 8 oz 15415 Kennel Vet VetRxDirect - Relief® Creme Rinse TropiClean Oxy-Med Medicated Oatmeal Rinse at PETCO
I think some of these come in spray form also