A baby crying is annoying and can drive you insane at times but a baby crying should not damage your ears or hearing.
The babies cries are not loud enough to really cause any hearing damage.
When my kids were babies I had to wear earplugs to help lower the crying noises when they were crying without needing anything.
The babies will eventually sleep through the night or stop crying as much through the day as they get older.
But then again as they get to the toddler stage they usually start screaming and crying again because they are frustrated or trying to get your attention.
I can understand that it gets frustrating hearing a baby crying or even a toddler crying no matter how much you love them.