Unfortunately there’s not a ton of rare quality swords around your level that aren’t random BoE drops(and thus rather low drop chances off several mobs).
As you get to high 30s you can get Sword of Serenity from In the Name of the Light for killing all of the final bosses in Scarlet Monastery. The quest chain starts in Desolace with Down the Scarlet Path.
Until then you might have to make do with greens.