Originally Answered: What is going on with my dog's skin, is it the shampoo?
It does sound like a reaction of sorts, possible a type of hives, to something in the shampoo. How long did vet tell you to continue the shampoo? No, I am not aware of red bumps being a normal reaction to shampoo.
What type of food are you feeding? Have you done any research into the BARF diet (raw food and bones) ? Does your food contain grains, potatoes, yeast ? Feeding raw changes the Ph of the body so as to not enable yeast to thrive. A commercial diet of meat, grain free, no potatoes, and no yeast can also have benefits. You might also want to look into apple cider vinegar (google apple cider vinegar in terms of systemic yeast infections) and the MANY benefits and uses of this, as far as changing the PH of the skin making it a very inhospitable environment for yeast to live.
One further thought. Yes, your environment makes a difference...warm, humid weather can absolutely play a part in the yeast situation. But you state that dog was ok for three years. His immune system is unable to fight off opportunistic yeast now. Diet change would be first thing I would check into (raw has many benefits) unless you feel that his diet is good as it is right now, as well as researching other types of things that support and strengthen immune system...and there are many options to research.
Check out apple cider vinegar; I think it could help this situation, especially if used in conjunction with other things aimed at eradicating a systemic yeast overload. And check into raw to see if you would consider it. The benefits are huge, especially when the main problem here is that the dog's skin is supporting yeast growth, and the way to turn this around is to make it so that skin will NOT continue to provide this area where yeast will flourish. While there are things that work from the outside like the shampoo, things that address the issue inside out (like food, supplements ) absolutely work to change Ph of the body.
I do not believe for one minute that this problem is done. Some yeast may have been eradicated, as well as an overlying bacterial infection. Stay on this with your vet and I truly belive that there are ways to work with this when you start to truly understand that the problem is partially one of the immune system and the body's inability to fight it off, and the skin providing a breeding ground for yeast overload.