Wa `Alaykum As-Salamu Wa-ramatullah Wa-barakatuh

Regardless of what type of hair you have, you need not to wash but the hair on the scalp itself, not the whole hair. That is the Hadith mentioned by Um Salamah asking the prophet (peace be upon him) and he answered that: “It is enough to wash your head three times.” (Muslim)

Almighty Allah knows best.