So sorry that you are going through this. Your boyfriend isn't being a supportive partner to you at all. He's not listening to you and he isn't taking care of responsibilities he has taken on.

You aren't responsible for his niece and you don't have to be, you don't have to be an unpaid babysitter, you don't have to take care of her. You aren't being selfish. You get to make your own choices, have your own opinions, your own wishes. You get to say No.

Unfortunately you've been unfairly placed in a situation where you are not allowed your own boundaries. Your rights are not being respected. And because his niece is not getting complete care, you end up by default the babysitter, if something happened while both of you are at the apartment, you are the adult and would have to deal with it. I wish your boyfriend would understand this.

If your boyfriend wants to help his niece, he needs to do so. You are an individual with your own rights, not an extension of him. And being supportive of him doesn't include being an unpaid babysitter when you don't want to be.

Moving can be stressful but then you can be in your own space, able to fully make your own choices.

Ideally when you told your bf that this isn't working, he would have sat down with you, listened, then worked with you to figure out what would work. He would have then worked with family and social services to find another place for his niece.