Mics were a variety of xlr and usb from rode, sennheiser and yeti over the past few years. Definitely in the frequency range but only moderate sensitivity at that freq and low to moderate self noise. Not exactly scientific but I would expect to see a bump of energy in the spectrum and get nothing.
A bit of searching lead to some DIY stuff using subwoofers (speakers) as the microphone input then some low-pass filtering and then fed to an op-amp.
Here's the link to the research paper on the elephant detector https://www.researchgate.net/publication/320596116_Eloc_Loca...
[1] https://www.youtube.com/watch?v=mekmsgjSqR4
I actually plan on recording sounds from my head, too. Could be weird spasms or something causing it, the lack of any variation in the two pitches makes that seem unlikely but possible.
I could imagine this logic also applying to other pumps in the house: AC pumps, baseboard heat circulators, sump pumps, etc.
What constitutes high quality microphones for you? Where these microphones that were made for this low frequency range?
EDIT: Especially on the microphones maybe the actual noise isn't 28Hz, but the 28Hz are harmonics of a 14Hz, 7Hz, 3.5Hz,... vibration. These harmonics may get produced inside some structures near your ear, explaining why you hear it and others don't.
You'd need special equipment to measure these low frequency vibrations.