So- basically you have to lie and not tell the truth of your life for her to be a friend?
It is very difficult when one person is TTC and the other already has children, especially if the TTC has been going on a long time/infertility issues.
It sounds like you were sensitive enough to ask/her to say that she wanted you to chat normally about it, but that turns out not to be true.
I am sympathetic though to the person TTC, it can be very very hard when your friends are all having babies and you are not. One of my friends chose not to visit me with a newborn due to this, but she was able to tell me and talk about it, and she certainly didn't restrict my conversation.
I am not sure where you go from here, try to see what she said less as an attack on you (even though it feels like i) and more about her deep personal pain (which is very real, and perhaps a bit distorted).
You have apologised, what more can you do? I'd be tempted to think that at the moment you can't be close friends, hearing about pregnancy/babies/tiredness of children is too much for her, and you don't want to not be yourself/able to talk about the things that are most important in your life either.
It's up to you, but I'd move back from the friendship, and let her know that you can't offer anything else than being yourself, and if that doesn't work for her, there's nothing you can do. Of course the other alternative is to plough on trying not to mention the things that upset her, and to listen to her a lot, but I get the feeling that your closeness will be damaged anyway.
Plus- if she goes on much more, she's milking it. She felt you were selfish, she said so, you said sorry, you need to go from here. If she wants grovel after grovel, let it (and her ) go.