Your doctor can also prescribe a topical steroid for this. These meds are available in a solution that is non-greasy for use on the scalp. The one I've used (and found very helpful) is fluocinonide solution. I also didn't do well with strong menthol shampoos or conditioners - they really irritated my skin even more. For me the best shampoo was Aveeno "Nourish & Volumize" shampoo and conditioner, and contrary to what many others experienced, my scalp itched far worse if I shampooed less frequently and felt best if I washed my hair every day. My dermatologist also advised me to shampoo daily and apply the fluocinonide right after shampooing. Good luck!
I agree with Dawn, and also, I would condition the scalp, with coconut oil, a day before I did wash it.
I also got a prescription anti-itch pill, it was called Atarax.
Try some shampoo and conditioner with tea tree oil and menthol.