I'm very sorry to be the one to tell you this, but after reading this and the other post about the birthday, I believe your girlfriend likely has Narcissistic Personality Disorder. (And I'm not talking about BS "likes to take selfies" narcissism - this kind is a real disorder.) And the kicker is that the people who have it the worst are the most incapable of recognizing that there is any problem. That is the thread I'm seeing in both this post and the other one, but holy isht, especially this one. Good gracious.
You be the judge. Please, please read all of these, do research of your own, and take some time to reflect on whether this is someone you want to remain not only in your life, but in your daughter's life. I know that you have made a big investment in time with her to this point, but I strongly, strongly encourage you to get out of this relationship sooner rather than later, for your own emotional health and for that of your child. Sending my very best wishes to you and your little one. Good luck.
10 Signs That You're in a Relationship with a Narcissist
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Narcissistic Personality Disorder