Hun, the feed-sleep-play "routine" really doesn't fit with most babies, and certainly not at that age. It's a lovely idea, but the reality is that they all have their own patterns and fitting in with them will always work out better than trying to get them to fit in with you.

At 3 weeks, most babies have no circadian rythm (ie day and night). But it does happen. The best thing you can do to get that happening sooner is feed her when she's hungry and put her to sleep when she's tired (and at that age sleep and eat is pretty much all she'll do).

It will all fall into place, but you need to give it time. For some babies it happens really early, others take a bit longer. I know how exhausting it is for you at the moment - we have all been there. It does get better, it really does. You just have to ride out these first intense weeks. Isn't it a shame no-one warns us about this!!