  We analyze the dynamical response of a two-dimensional system of itinerant
fermions coupled to a scalar boson $\phi$, which undergoes a continuous
transition towards nematic order with $d-$wave form-factor. We consider two
cases: (a) when $\phi$ is a soft collective mode of fermions near a Pomeranchuk
instability, and (b) when it is an independent critical degree of freedom, such
as a composite spin order parameter near an Ising-nematic transition. In both
cases, the order-parameter is not a conserved quantity and the $d-$wave
fermionic polarization $\Pi (q, \Omega)$ remains finite even at $q=0$. The
polarization $\Pi (0, \Omega)$ has similar behavior in the two cases, but the
relations between $\Pi (0, \Omega)$ and the bosonic susceptibility $\chi (0,
\Omega)$ are different, leading to different forms of $\chi^{\prime \prime} (0,
\Omega)$, as measured by Raman scattering. We compare our results with
polarization-resolved Raman data for the Fe-based superconductors
FeSe$_{1-x}$S$_x$, NaFe$_{1-x}$Co$_x$As and BaFe$_2$As$_2$. We argue that the
data for FeSe$_{1-x}$S$_x$ are well described within Pomeranchuk scenario,
while the data for NaFe$_{1-x}$Co$_x$As and BaFe$_2$As$_2$ are better described
within the "independent" scenario involving a composite spin order.
