So what's stopping you from doing your colors by hand, too? No markers, paints, or colored pencils?

Can you access a basic scanner? Most printer/copier combos can scan, and you can also usually find one to use at public libraries or any print shop. If you scan your drawing, then you can set it to 'multiply' and do all your colors underneath it with very little effort and no manual tracing required. I'm sure the digital artists here have lots of tricks to make it go even faster.
If you really feel that you must trace the drawings by mouse, try using a vector painting program, that'll let you get those smooth lines you want.
But even lacking those tools, here's my 10 minute GIMP edit, mouse only, based on your photo:

Lack of tools is a challenge to be solved, not an insurmountable obstacle.