You said she is depressed and has social anxiety. I suggest that you're expecting too much from her. She may not be able to meet your expectations. I think her reasons for not attending the baby shower are valid. She was up half the night and didn't feel good because she is depressed and has social anxiety. Why does she need to outline the details for you?
The way you manage this is to focus on changing your expectations. You don't need to detach from her. You need to detach from your expectations. Know that if she's having difficulty in her life she is not going to be able to make you a priority. Know that you'll have to be direct with her when you need her help. When you call tell her you're having a difficult time and you'd like for her to just listen, for example.
Know that you don't understand how her emotional deficits work. In my experience it's easier to show a great personality when out and about. I'm relieved to have friends who accept me as I am and don't expect me to keep up that front when I'm with them.
Stop making the extra effort. This is another situation that would benefit from understanding the co-dependent relationship. If you're comfortable with yourself and have a wider range of relationships then with her you would be comfortable getting what you need from someone else. When you don't need for her to act in a certain way, your relationship will become more relaxed and you won't be so hurt.
Perhaps this isn't a relationship that will work for you. It sounds like you don't really understand and accept her as she is. You expect from her actions that she's not able to give you. You don't need to understand her anxieties. You know she has them. Accept her as she is, anxieties included.
It sounds like you're hurt because you think she's not being honest with you. You think that she doesn't really have social anxieties because she acts one way with a group and a different way with you. I suggest that you're possibly not being honest with her, either. You were hurt when she didn't come to your baby shower. Did you tell her how you felt at the time? Sounds like you continued feeling hurt and then only called her when you were moving to her neighborhood. And when you weren't able to talk because of the moving and the other people present you left it to her to bring up the subject again.
This is also another example of how texting does NOT work. You told her you were hurt in black and white. Feelings are not black and white. We have to talk about them in all there nuances. In essence you told her she was wrong without offering any way of resolving the issue.
If you want this relationship to work, stop texting. Get on the phone, tell her you're sorry that the friendship hasn't been working and ask to get together over coffee to talk about it. Then, really try to see things from her viewpoint. Yes, give your viewpoint using only I statements. I felt hurt when you did such and such. I thought you were able to come but didn't want to come. Then give her a chance to explain how she was feeling in more detail.
Do not bring up that situation with the baby shower last year. Stop thinking about it, even. I suggest that the hurt you felt then is continuing to hamper your relationship now. I urge you to deal with that situation by focusing on the way you are thinking about it. Try to accept that she was unable to come for the very reasons that she gave you and let go of your pain.
Please read a book on co-dependency. I think you'll find that you will grow and have better relationships once you learn to rely on yourself, learn how to be assertive, and stop expecting someone else to make you happy.
Perhaps if you could love this friend well enough you wouldn't need to keep score on how one sided the relationship is? We do for others, in love, without expecting something in return.
It's true that we have to let go of some relationships because they are one sided. I'm suggesting that you might consider this as an opportunity for you to grow.