A single sensor with a piezoelectric quartz transducer is considered a platform for simulating an “electronic nose” that performs the function of a sensor array. The analytical task was to detect volatile organic compounds, component-by-component, in biosamples at diagnostically relevant concentrations without selecting mixtures or any sample preparation. We confirmed the fundamental possibility of utilizing a single sensor for the separate detection (recognition) of vapors of organic compounds and various functional states of a body during a short contact (60–80 s) with skin, the most representative and constantly performing bioassay. Modifying the electrodes of bulk acoustic wave piezoelectric quartz resonators with 2–4 μg of the nanohydroxyapatite phase is an essential step in solving the problem. The newly calculated adsorption kinetic parameters can be used to detect biomarkers of many diseases with high reliability, including С3–С5 alcohols, ketones, linear and cyclic amines, acids, aldehydes, etc. The hydroxyapatite sensor can detect molecules pointing to problems with many organs, and any abnormalities in the functioning of the nervous and cardiovascular systems. It can also measure the body’s responses and compensatory mechanisms in relation to stress, hunger, and fatigue. The sensor has a potential as a simple diagnostic and monitoring tool for point-of-care diagnostics of both adults and children.