Measure square waves without oscilloscope?
If you got some electronic parts, then you can make a circuit that makes an LED that gets brighter with frequency.



Link to schematic.


Upper graph = current through LED, more current => brighter
Bottom graph = what you are trying to measure


In the simulation I am using a frequency sweeper as the input to see how the circuit behaves to different frequencies. As you can see, the higher the frequency, the brighter the LED gets. 

This one won't really care if it's square waves, triangle waves or other forms of waves. As long as their amplitude is above 1.4 V and above 1 kHz, then you should see the LED light up.

If you increase the size of the 1 nF to something larger, then the LED will light up with lower frequencies.

The transistor isn't magical, it won't make the LED burn up. The 1 kΩ resistor in series with the LED will limit the current.

If you have very few parts, then you can remove the 1 µF, 10 kΩ resistor and the diode pointing to the right. But if you do that, then the LED might be too dark.



Edit

You could also remove the LED, the 1 kΩ resistor, the NPN transistor and connect the 10 kΩ resistor to the ground so it is in parallel with the 1 µF capacitor. You can then measure the voltage across the 10 kΩ resistor which might be easier to read rather than the brightness of an LED. 

That circuit I just described is almost an envelope detector. 

This is the circuit I'm talking about. 




Upper graph = Voltage across 10 kΩ resistor
Bottom graph = frequency sweeper, in your case the signal you want to measure.


Here is the circuit I'm proposing, black on white. Not hidden behind words.