Saving for a Rainy Day

Here's where I'm really going crazy. It's absolutely one of those things that has me unsure of what in the world is going on in this brain and heart of mine. Lately, I've become increasingly more and more unsure if the time tested idea of saving for a rainy day is actually Biblical. I'm ALMOST to the point of being fairly sure in some ways it's not.
Going back to Matthew 6, verse 34, where God is speaking about providing everything we need, even the basics, he says:
34Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.
Then there's the old testament story of manna. Remember the principle God taught the people there. He provided for them one day at a time. In fact, anyone who tried to get just a little extra for the next day, found a nice jar of nastiness in the morning.
And there was a certain rich fool in Luke 12:13-21. He was going to build some barns for all he had saved up. That didn't go so well for him if you read the story.
Is it really related? Well, keep reading again in Luke. It's back to the do not worry about what you'll eat drink or wear as related in that book, so, yeah, I think it definitely is.

What does all this exactly mean? I'm still working on that part. And still praying. But something tells me things cannot just remain the same. And, if you did keep reading in Luke, don't worry. Verse 12:33 scares me a bit also.