This is actually a pretty common problem. A lot of adult humans have a lactose allergy. Lactose is the milk sugar naturally found in dairy products. Everyone has different responds to allergic reactions. Some people will experience GI issues, some people with get acne, some people will get a skin rash. It's all very individual.
There are two main types of whey protein available: a whey protein isolate and a whey protein concentrate. The problem with a whey protein concentrate is that it will contain a few grams of lactose (the milk sugar naturally occurring in dairy products) per serving. The majority of adult humans have a lactose sensitivity which can cause GI issues, acne, skin rashes etc. A whey protein isolate on the other hand is essentially pure protein and will have no lactose.
When purchasing a whey protein isolate you want to see nothing in the ingredients list besides whey protein isolate, natural flavours, a natural calorie free sweetener like stevia and maybe some salt, cocoa powder and soy lecithin.
I personally use the whey protein powder isolation from n2bm.com. A 30g scoop has 26g protein, 1g carbs and 0g fat.
Switch to a pure whey isolate protein and I suspect your skin rash will go away.