Measuring frequency response range of piezoelectric disc
I am afraid that it is rather impossible without a proper hardware. Sweep sine is ok as a general method, but you would either need:


Reference transducer with known (preferably) linear frequency response. Then you can find the difference between those two.
Signal actuator with known frequency response, and then you can also find the difference between recorded signal and what it should be.


In any other case you will only measure the convolution of actuator response and response of piezoelectric element.

You should also understand that this disc is meant to be used as a contact device, not for recording of sound waves. There is a huge difference between those two signals recorded.

Lastly you can try to search for frequency characteristic of known model (presumably measured by someone). I did similar work back in time, but we used different type.