Can I make a step up transformer using these components?
Yes, a transformer will worth the opposite when connected backwards.

You have a roughly 16:1 transformer - for every 16 volts you put in you get 1 volt out.

In a perfect world, for every 1 volt you then put in the secondary you'd get 16 volts out of the primary. So 5V p-p would ideally give 80v p-p out.

However, it's not quite that simple.

Transformers are designed to work most efficiently at certain frequencies.  To get the most out of your transformer you should run at 50Hz, not 100kHz.

Also you ask if it will be a square wave out.  No, it won't.  It'll be a wave at the same frequency as the input, but it will be far from square.  It would look more like this:



You get big peaks at each edge as the magnetic flux changes, but while it's stationary (during the flat bits of the square wave) the induced current in the transformer quickly decays.  To get a faithful representation of your input waveform you would have to limit yourself to a constantly changing wave, like a sine wave, or triangle tooth wave.  A saw tooth wave would work, but the rapid flux change at the vertical edges of the teeth would probably get a bit spiky.