welcome to the site. Yes most on here uses computers for their mapping, no matter if the place previous made elements (or stuff made by others) or hand draw it all themselves. A few makes handdrawn maps the "old fashioned way" ie. with pencil/ink/etc, but please bear in mind, that you can also handdraw with a tablet connected to your computer.
For lettering you can do Gimp (pixel based) or another free program is Inkscape (vector program).