Ivy

You can try the Lush shampoo bar for dry skin in the scalp area, I think it's called Soak & Float but the Lush assistants can help you. It stinks like a bonfire but it's the only thing, including prescription shampoo, that has helped my scalp. I had horrific redness and dry patchy skin on my forehead, neck and even my ears before I used this shampoo, I could see a difference the first time I used it.
The way you describe your problem it does sound like rosacea so I would suggest a dermatologist but don't be put off if the one you saw did not help, there are good and bad doctors. Ask around and try another dermatologist.
The other thing that did occur to me is that you could be allergic to something, allergies do not always take the form of hives etc. I honestly think a doctor should evaluate all of your symptoms.