I think you will struggle to find those regional shapefiles. But when i've needed country wide shapefiles, i tend to use Natural Earth:
In your case, i would download the "Admin 0 - Countries" file. If you then open this shapefile into, let's say QGIS or ArcMap, open the attributes table and ...
r.sim.sediment is a tool from the GRASS toolbox. You can find documentation for GRASS tools by clicking the "Help" link in the QGIS tool dialog for that tool, or go straight here:
It shows that you need a few raster data sets over your study area, including elevation, water depth and so on.
There are lots of places to download GIS data and imagery around the web but they can be tricky to find. Earth Explorer is a good option that searches by location, time, and data set, giving you access to lots of imagery for free. This includes imagery from NAIP / NAPP, which is probably the most applicable to your project.
You may want to check out the relatively new MERIT-DEM, which is mostly SRTM but heavily corrected (especially north of 60 degrees). You can download it in tiles. They also have corresponding hydrologic models (MERIT-Hydro) that include flow directions, flow accumulations, channel widths, height above nearest drainage, and a depression-filled DEM. All global....
There is the Open-Elevation API (https://open-elevation.com/) that looks promising
for API examples
Live API sample:
For those continuing to search (I was and landed here). There is a free USGS service which is well buried. Link here. Worked for my use case of a couple of dozen points. HT to @barrycarter for the index link.