[Gwathagor]

Of course, Tolkien isn't going to put ALL the waterways on the map...just the really major ones. I think that we have to assume that a river that swells as large as Anduin does further south must have more than 3 or 4 smaller streams/rivers that flow into it. So it's plausible, but hard to prove.

One other thought: the woodmen's settlements are a good indication that there are, in fact, streams flowing out of the forest into Anduin, since one of the most basic human needs is water. Any decent habitation has a nearby water source.