I'm not sure if there is a god of childbirth but the goddess of childbirth is Artemis.

Yes, Artemis was a goddess of childbirth.

Elizabeth Fenwick has written:

'Childbirth' -- subject(s): Pregnancy, Childbirth, Popular works

'Childbirth' -- subject(s): Pregnancy, Childbirth, Popular works

Bes was protecting god of childbirth, Taweret was the ancient Egyptian goddess of maternity and childbirth, protector of women and children.

The hymen doesn't increase in size after childbirth. During vaginal childbirth the hymen is often torn.