As the "Weird thing"/"Both [would be] legitimate" anon from above, I have to say that if you don't like the way the friendship is going, you have no obligation to continue it. If you bring up that she should seek help, remember to sound as nice as possible. Not only will it make your friend more likely to listen, but it'll make cutting ties if she gets mad feel more like the right thing to do.

(I would also add that maybe you should try to look at why your friend is getting mad and just figure out what looks legitimate and what seems a little much. I tend to... try to empathize. Emotions are emotions and they can be hard to control, which is why I'm saying this.)

But seriously, you're not obligated to do anything you don't want to, and that's the big thing here.