Did I damage my undercarriage?

,

You didn’t mention if there was any change in the car’s performance after the incident, but…
if there is no change in the car’s performance…
if there are no leaks (I REALLY hope that you are personally monitoring fluid levels, rather than just assuming that there are no leaks because you see no fluid leaking!)…
if there are no unusual noises, and…
if there is no visible physical damage…
…then I think you can safely assume that all is well.

Incidentally, the car’s computer only monitors emissions and related functions.
There is no trouble code for, “you drove over a spike”!

But, in any event, you should carefully check the levels of all of the car’s fluids.