Hello Leo
Katie's right. You're not responsible for her happiness. You can want her to be happy and try to help her but in the end there's only so much you can do.
It's important that you watch out for yourself. Sure you want to be there for her all the time, but when its making you depressed maybe it's better to talk with her and set some boundarys. It's not good if she only relies on you for support. She needs to find other people, maybe the school counselor, a teacher or a friend she can also rely on because if she only depends on you then in the long run it will hurt the both of you a lot.
So no your not being selfish or senseless. Not at all. Your great for sticking with her and trying to support her.
But to support her you have to keep yourself safe as well.
Maybe you can talk with her about the date thing. Maybe you can make an agreement, that you talk over phone everday or something and only meet up once a week? It's just one suggestion for a compromise and I'm sure you'll be able to find a better one that works for both of you.