Are we moving too fast? does she still love me?

hmmmm.well, because I have had similar situations, I would start asking more pressing questions about the granma----what hospital is she in, and if you find out, call the hospital to see if there is really a person by granma's name there.
If she is telling the truth, maybe she does need the time with the family. However, is not like you can be with family 24/7.
To avoid any miscommunication, I suggest that maybe you ask her when she wants to be contacted again; let's say you give her space for 2 weeks and then you call her; what if she then goes psycho on you and tells you that you never called her? Women are a bit crazy sometimes, so I would maybe say something like, 'i understand you need time with your family. When then would be a good time to get a hold of you? I don't want to be a pest if you need time with family and if you need space, that's not a problem; I just want to know a time frame so that we don't miscommunicate.' That's a bit too long but maybe you get the point.