First of all tell your mom that you need one because it puts you at a great disadvantage to other runners in pacing, HR monitoring, distance monitoring etc. If you can't afford a real GPS you might look in to the Nike IPOD sensor if you already have an iPod. Not sure how accurate they are as I've never used one but they go for about 20 dollars. Also a cheap pedometer would do about the same.
Now to tell you how we did it in the old days.
-drive it in a car and use odometer to track distance, pick out land marks at mile markers and memorize them for example a tree or stop sign might be your 2.5 mile out marker. Mark out a few routes that you run on a regular basis and when you run them recall what mile marker you are at all along the way. Combine this with a digital watch which costs as little as a dollar and you have a pretty well calliberated time/distance run.
-go off time, obviously you won't be able to drive every route before you run them but if you can just time your self and roughly calibrate it by your pace ie if you think you are going 8 min per mile and you run for an hour you ran roughly 7.5 miles. It may not be super accurate but really for most runs its good enough. And then you can do like everyone else on let's run and claim you are running 110 miles a week.
-measuring wheel, if you need to be super accurate for workouts buy a measuring wheel and mark it off. They sell them at home depot for about 40-50 dollars which is I know still almost as much as a cheap GPS but it will probably be even more accurate for short distances.