I agree with all those who have told the OP to be patient and wait for an invite. You are not the important one here, your wishes/wants come miles down the list of importance to a new mother.
When I had my 2 children (over 30 years ago), I made it clear to EVERYONE that I didn't want any visitors in the hospital and that EVERYONE must wait until invited to visit us at home.
Everyone complied with my wishes, that is, with the exception of my mother and sister. They said they had a RIGHT to see the baby (on both occasions). Needless to say, I was absolutely fuming because everyone else was prepared to wait until we were back home and settled.
Because of these breaches of trust, I made sure that my mother and sister didn't get invited to see either child for 3 months and 9 months respectively. I knew my mother was the instigator of the visits, but she wouldn't have been able to get to the hospital (on either occasion) without my sister skiving a day off work to take her, so I made her wait longer because she SHOULD have said "No mum, Harmonypuss said no visitors and to give her time to get to know the baby", but she didn't.
So the moral of my story is to stay in contact with the new mum and just play it by ear because if you overstep the mark, you could be pushed away for a lot longer!