Yeah, doing the shadowing in Photoshop is just so much easier because of the layers and opacity settings. Changing the opacity allows you to adjust the transparency of the layer so that you can just add shadow above your drawing.
The alternative to Photoshop is a free program called GIMP
. It has many of the same options as PS, and is more than equipped for doing this kind of work. Layers, Opacity, better magnification, Brightness/Contrast, multiple Undo/Redo, ability to save in Indexed Colour, etc. The main reason I use the Paint/Photoshop combo is because I've been drawing pixel art for almost a decade with these programs, and I've become very comfortable with them. If I were you, I'd absolutely give GIMP a shot since it's free and capable.
Edit: Kickass University Hospital!