why does FeCl₃ have such a specific smell?
The only clue I have been able to find is a one-off sentence in the Wikipedia article for $\ce{FeCl3}$, for which no reference is given:


  Iron(III) chloride undergoes hydrolysis to give an acidic solution.


If so, then the reactions are probably those along the conversion of $\ce{FeCl3}$ to $\ce{Fe2O3}$, producing hydrochloric acid $(\ce{HCl})$. The hydrogen chloride gas that escapes from the solution has a pungent acidic acrid smell. 

Possible reactions include:

$$\ce{FeCl3 + H2O &lt;=&gt; FeOCl + 2HCl}$$
$$\ce{2FeCl3 + H2O &lt;=&gt; Cl2FeOFeCl2 + 2HCl}$$
$$\ce{2FeOCl + 2H2O &lt;=&gt; Fe2O3(s) + 2HCl}$$

Because these reactions are in equilibrium, solutions of $\ce{FeCl3}$ can be stabilized by addition of $\ce{HCl}$. Addition of $\ce{HCl}$ also promotes the formation of the tetrachloroferrate ion $\ce{FeCl4-}$, which is more resistant to hydrolysis.

$$\ce{FeCl3 + HCl -&gt; FeCl4- + H+}$$

Ferric oxide (Iron(III) oxide $\ce{Fe2O3}$), is insoluble. Does your solution develop reddish precipitate as it ages? That would be  evidence in favor of hydrolysis as the source of $\ce{HCl}$.