Coupling a microscopic mechanical resonator to a nanoscale quantum system enables control of the mechanical resonator via the quantum system and vice-versa. The coupling is usually achieved through functionalization of the mechanical resonator, but this results in additional mass and dissipation channels. An alternative is an intrinsic coupling based on strain. Here we employ a monolithic semiconductor system: the nanoscale quantum system is a semiconductor quantum dot (QD) located inside a nanowire. We demonstrate the resonant optical driving of the QD transition in such a structure. The noise spectrum of the resonance fluorescence signal, recorded in the single-photon counting regime, reveals a coupling to mechanical modes of different types. We measure a sensitivity to displacement of 65 fm/ limited by charge noise in the device. Finally, we use thermal excitation of the different modes to determine the location of the QD within the trumpet, and calculate the contribution of the Brownian motion to the dephasing of the emitter.