My beard had gotten unbelievably itchy between weeks 2 and 4, what helped was using lots of Jojoba-oil. Jojoba mixed with 5% Tea Tree oil worked as well. The itching will pass after a while.

I have written a bit about different beard products here:
moustache cups and mugsbeard brushes and combs
beard literature | simple homemade beard oil

my beard journey | my bart * aber herzlich beard oil | Bartöl store (external link, not affiliated with or endorsed by beard board)