confused

To any ladies with a negative blood type-so I have type 'A negative' blood. They are going to give me a rhogram shot on Monday, I was told that even if my blood mixes with my baby's blood that it can not affect your first pregnancy. (This is my first pregnancy)
ALSO, I read somewhere that they try to induce you at 37 weeks with a negative blood type to try and prevent the placenta tearing later on in your pregnancy (37+ weeks). Is any of this true?
Can anybody give me any piece of advice or history they know on this?
Thank you:)