B’sha’ah tovah!
You are correct that the Torah stipulates different waiting periods for a boy or a girl. However, subsequent rabbinic enactments require that the process of becoming tehorah begin only after postpartum bleeding has ceased. As most women bleed for a number of weeks after childbirth (the median is 3-4 weeks), it is very unusual for there to be a difference in real life between a boy (where the minimum time before mikveh immersion is 12 days) and a girl (where the minimum is 14).
Like all women, the yoledet (woman who has given birth) must perform a hefsek taharah and count seven blood-free days (shivah neki’im) before she immerses in the mikveh. She may perform her hefsek taharah as early as the fifth day from the onset of her niddah status. If she gave birth to a girl, however, she may not immerse in the mikveh until 14 days have passed since the birth. As we said, most women actually immerse much later, since the hefsek taharah cannot be performed before all bleeding has ceased. A woman may immerse once her clean days are complete, whether or not she is ready to resume relations immediately.
Until the woman has immersed, all the laws of niddah apply, including not sharing a bed or blanket. This can be a challenging period. You may find some of our answers posted on the site to be of help. You may also wish to watch our video on the topic, Niddah in the Postpartum Period.
BeSha’ah tovah!