baby losing hair

I have a 5 1/2 month old and he's been losing so much hair in the last week and a half. He's still got a bit of cradle cap, maybe that has something to do with it? I usually put a bit of coconut oil in his hair/scalp and now when I do that my hands are covered in hair. I know that newborns lose their hair but does anyone know if it's normal at this age?