This subject can indeed be quite confusing, as I got confused a bit myself as well reviewing the theory. So lets review the basics first:
The Basics
The complete formula for the mass flow through a convergent-divergent nozzle, assuming ideal compressible flow, is as follows (see this NASA link for the derivation):
$$\dot{m}=\frac{A\ p_0}{\sqrt{R\ T_0}} \sqrt{\gamma}\ M\bigg(1 + \frac{\gamma-1}{2} M^2 \bigg)^{-\frac{\gamma+1}{2(\gamma-1)}}$$
With $A$ the cross-sectional area, $p_0$ the upstream total pressure, $R$ the mass specific gas constant, $T_0$ the upstream total temperature, $\gamma$ the ratio of specific heats and $M$ the Mach number.
It is important to realize that our previous formula doesn't specify at which point in the nozzle we evaluate the mass flow. We don't really care as we know the mass flow should be the same throughout the nozzle through the conservation of mass: mass cannot just disappear. Nonetheless for $A$ and $M$ it does matter and they should be given for the same point. Which we'll see is important later.
Now if you take the derivative of this equation with respect to $M$ and set the result to zero, one finds the maximum value for $\dot{m}$ is found when $M$ is 1 (again, see NASA link). So, one says: the maximum mass flow rate is found when the velocity is sonic and we call this maximum flow: choked flow.
If we fill in $M=1$, we get the following formula for choked flow:
$$\dot{m}_{max}=\frac{A\ p_0}{\sqrt{R\ T_0}} \sqrt{\gamma}\bigg(\frac{\gamma+1}{2}\bigg)^{-\frac{\gamma+1}{2(\gamma-1)}}$$
Now we know that the flow velocity in a choked nozzle is sonic at the throat*, so $A$ and $\dot{m}$ are both evaluated at the throat**. Also, for clarity, let's replace all $\gamma$ terms by the Vandenkerckhove-function, $\Gamma$, to end up at the final formula for the mass flow through a convergent-divergent nozzle:
$$\dot{m}_{max,\ throat}\ \ \ =\frac{A_{throat}\ \ p_0\ \Gamma}{\sqrt{R \ T_0}}$$
Answer
Having arrived at this final formula it is quite clear that decreasing the throat area indeed reduces the mass flow rate, as you already stated, while the flow velocity at the throat (the end of the converging part of the nozzle) would remain sonic.
However, nothing is preventing us from increasing the upstream pressure and thus increasing the mass flow rate. Inversely, "increasing the mass flow rate" (not sure how one would do this directly) would increase the upstream pressure, all else being equal. So mass wouldn't "accumulate", but your intuition isn't wrong: increasing the pressure would eventually explode your nozzle!
Additionally, our flow velocity at the throat would remain sonic, so the density of the flow must increase to increase the mass flow rate. This is possible, because we've assumed compressible flow at the start!
Hope this answer helps, just comment if it still isn't clear and welcome to the space stack exchange!
* Choked flow, and consequently sonic conditions at the throat, only happens if a certain pressure-ratio is achieved (see below), otherwise the flow through the whole nozzle is subsonic
** We know the mass flow is equal throughout the nozzle, so in general one can say $\dot{m} = \dot{m}_{max,\ throat}$, but I've kept it intentionally specific to prevent misunderstanding
$\frac{p_e}{p_0}=\bigg(\frac{\gamma+1}{2}\bigg)^{-\frac{\gamma+1}{2(\gamma-1)}}$
