High-Q photonic microcavity sensors have enabled the label-free measurement of nanoparticles, such as single viruses and large molecules, close to the fundamental limits of detection. However, key scientific challenges persist: (1) photons do not directly couple to mechanical parameters such as mass density, compressibility, or viscoelasticity, and (2) current techniques cannot measure all particles in a fluid sample due to the reliance on random diffusion to bring analytes to the sensing region. Here, we present a new, label-free microfluidic optomechanical sensor that addresses both challenges, enabling, for the first time, the rapid photonic sensing of the mechanical properties of freely flowing particles in a fluid. Sensing is enabled by optomechanical coupling of photons to long-range phonons that cast a near-perfect net deep inside the device. Our opto-mechano-fluidic approach enables the measurement of particle mass density, mechanical compressibility, and viscoelasticity at rates potentially exceeding 10,000 particles/second. Uniquely, we show that the sensitivity of this high-Q microcavity sensor is highest when the analytes are located furthest from the optical mode, at the center of the device, where the flow is fastest. Our results enable till-date inaccessible mechanical analysis of flowing particles at speeds comparable to commercial flow cytometry.