Sorry - but you are wrong in thinking the Swanfleet is a river in West Rohan, or in Rohan, at all. Neither is it east of the Isen - it's west of the Isen's source and north of the Isen itself as it flows to the sea.
Swanfleet is the name given to the River Glanduin where it flows through the fens just northeast of Tharbad. The Sirannon (Gate Stream) that flowed from Khazad-dum was a tributary of the Glanduin.
Eregion bordered these two rivers on the north, and Dunland bordered them on the south.
They do not flow in Rohan.
The Deeping Stream, on the other hand, ran around the base of Helm's Deep on the south and east sides:
Quote:
|
The stream that rose in the gorge of the White Mountains known as Helm's Deep. It flowed through a culvert in the wall that guarded that refuge of the Rohirrim, and then around the feet of the rock where the Hornburg stood, before beginning its journey into the wide lands of Rohan.
|
-- Encyclopedia of Arda
You can also investigate the Rohan rivers by looking at
The Atlas of Middle-earth; pg: 88 - 89. And the Deeping Stream in the same Atlas, pg. 132 - 133.
HERE is a map you can use to look at the locations of the various rivers. You can click on it to enlarge it.
~*~ Pio