Understanding Responsivity of an IR sensor paired with a black body IR emitter
Do I need to check now on the graph of the Responsivity the value for
  my Frequency, which is, if the wavelength is 4.5 μm, 222 kHz?


No, whatever power enters through the window of your detector, the detector converts that to a voltage in the ratio of 150 volts per watt.

So, if all 4.2 mW entered the window, you would get a voltage change at the output of 0.15 volts per milliwatt or about 600 mV.

Looking at the data sheet, I believe you meant to write 150,000 volts per watt for the detector’s responsivity.