OK, so the amazon basin is essentially one huge bowl. If you think about rain falling in a bowl, it always travels the nearest, steepest path to the middle.

In terms of the reasons rivers give themselves a serpentine shape is that they are in a long, mostly flat area, and they carry a lot of particulate matter (silt, salt, dirt, etc). the fastest water carries more of it, and, like a merry-go-round, it travels on the outside of curves. this carves curves wider - meanwhile the slow water can't carry as much of the particulate matter, and travels on the inside of the curve - and since it can't carry as much, it dumps the excess. the shape evolves because the water still tries to go down hill the fastest way possible.

So in terms of your map:

1) tear out the rivers and lakes you already have.
2) map your elevations in depth first. (pun intended!).
3) give yourself an extra layer and map out the fastest points to the lowest common grounds.
4) draw the rivers in. Remember that rivers make a Y shape, rather than a T.

if all else fails, there's a thread about rivers in the resources section of the forum that's worth reading.