With so many billions of us on the planet dreaming about things that are important to us it's really common that at least some of the the things we dream about will actually be the 'real end result'. We don't tend to dream about unrelated things like the political situation in Burma. We tend to dream about things important in our own lives. And since those events do actually have a resolution, if we dream about the way things DO resolve, we remember it clearly.
I have many, many dreams about real worries in my lives and sometimes they come true, and sometimes they don't, because that's how life works. Sometimes things go well and sometimes they don't. I'm VERY sorry to hear about the sad way your situation turned out, but it does sound like it was a probably end result given what happened. And your fear was that it would happen. The way you reacted in your dream (running out of the house) is based on your personality. You didn't run to the basement or just stay still. It's your personality to run out of the house. So you did that in your dream, and you did that in real life. In the same manner, it's your brother's personality to go after you and not just let you "cry alone". So in your dream you knew he'd come after you to help, and in real life he did that too.
It'd be like if you had a dog that was always by your side. If you dreamt that your dog was by your side, and then in reality your dog was by your side, both would be a reflection of the real life personality of your dog. It wouldn't be that you dreamt something "incredibly unrealistic". You dreamt about the way your dog *is*. In the same way, you dreamt about the way your brother *is* and the way that you *are*.
It's always a great idea to keep a dream journal to help you explore your dreams to learn more about what concerns you in your world, and how you faced it, and to think about it. If you had kept a dream journal about this dream you might have noted that you were really afraid that your cousin's baby would die. You'd note that if that happened, it'd probably be your mom who sat down and told you. You'd also note that if you heard that news, your reaction would be to try to run away from it, because you didn't want to talk with your mom about your pain, you would want to get away from everyone. And you'd then note that it would be your brother that would come after you, because that's the way he is, and would comfort you.
Dream journals can really help you talk about issues that you're worried about, so that you can either find a way to solve the fears or, in this case where there wasn't anything you could do to "make things better", just be able to talk about things with your family. A lot of times, talking about things can make it easier to handle.