After I had my baby, a lot of my hair started falling out and my floor is full of hair.
After I had my baby, a lot of my hair started falling out and my floor is full of hair.(産後たくさん髪の毛が抜け始めて、床が髪の毛でいっぱい)
上記のように説明的に表現されると自然かと思います。
産後はpostpartum、抜け毛はhair lossとも表現できます。