I guess?
No idea what the rest of the layout is, or where the probes were connected. Looks like there are hidden pours, and I guess internal pours/planes too?
Your derivation I think is about right, also it ends suddenly after a half wave, I think because the input capacitor is overcharged as a result, and current is prevented from reversal by the diode (which I guess is not jumpered out on your assembly). Your derivation does not include resistance, which, it's not obvious how much resistance there should be here, probably just some milliohms.
Note that the impedance includes paths from the power source, and to the scope probes. I don't know how you have everything wired up. Trace the real network and solve for that.
Aside, interesting that it looks pretty linear (sinusoidal). Ceramic capacitors generally lose value with increasing voltage, distorting the waveform. It may simply be because we're seeing inductor voltage here, dunno.
As for values, C is probably around 3x4.7uF and L needs to be calculated from wiring lengths, or the waveform. Evidently iL(t) = 0 after 18.4us, or (18.4us)/sqrt(LC) = pi.
Tim