so the fundamental question to me is: Do you want to create a real fantasy (here: fictional) map that has nothing to do with reality or create just a fantasy like map style?
If the first one is what you want, you can make use of existing OSM technologies (editors, renderers, ...) or general free GIS technology (QGIS, OpenJUMP, ...) to create and visualize such a map. But please pay attention that you don't upload your stuff to the OSM DB as it doesn't reflect the reality and might destroy the work of others! So you download an OSM area with JOSM editor, erase everything and work local with this .osm file that now contains all your fantasy world.
If you just want to present/recycle your existing drawings, you need to convert them to a raster image like .PNG and make use of a webmap toolkit to present it in your browser. As everything is fictional, you don't need/have a coordinate system or map projection or you just use the defaults like for Google Maps. With OpenLayers, it might work like this.
For the second one, you might play with existing (offline) renderers like Tilemill or Maperitive. There are also some nice artistic/fantasy map styles that might already fit for you: