Gate and Drain ringing on a highside MOSFET Driver
Your probing is awful and high frequency currents in the switching circuits will induce voltages in the loop area formed by your probes. This is what people use when testing circuits like this: -



The spring wire on the earth part of the probe ensures that the loop area you probe is quite small. In other words use a proper oscilloscope probe and a ground spring.

Next, when the MOSFET goes open circuit to interrupt current from the 12 volts into the 33 uH inductor the drain-source capacitance of the MOSFET remains in circuit and this might be several hundred pF. This will form a resonant circuit with the 33 uH inductor and you will get a decaying sine wave at high frequency. This is normal.

It's also normal for the inductor to have a self resonant frequency (due to inter-winding capacitance) that also causes (or adds to) the ringing you might see.

That decaying sine wave can also couple to the gate via the MOSFETs drain-gate capacitance and you can observe a small effect on the gate although I think your biggest problem is probing.