Itching of Beard depends on two factors-

  1. The Number and Type of Micro Organisms in the Beard
  2. The Sensitivity of the skin

So, More Microbes = More Itching & More Sensitivity = More Itching

Of these two, sensitivity of the skin is something you were born with so you cant change that very easily. 

But you can reduce the number of microbes by Washing. Just increase the frequency and duration of washing your beard. You will see a reduction in itching 

Only if Increased frequency and duration of washing does not improve, we have to follow other steps.