  We present a comprehensive ultrasound study of the prototypical heavy-fermion
material CeRhIn$_5$, examining the origin of the enigmatic 30 T transition. For
a field applied at 2$^\circ$ from the $c$ axis, we observed two sharp anomalies
in the sound velocity, at $B_m \approx$ 20 T and $B^* \approx$ 30 T, in all the
symmetry-breaking ultrasound modes at low temperatures. The lower-field anomaly
corresponds to the well-known first-order metamagnetic
incommensurate-to-commensurate transition. The higher-field anomaly takes place
at 30 T, where an electronic-nematic transition was previously suggested to
occur. Both anomalies, observed only within the antiferromagnetic state, are of
similar shape, but the corresponding changes of the ultrasound velocity have
opposite signs. Based on our experimental results, we suggest that a
field-induced magnetic transition from a commensurate to another incommensurate
antiferromagnetic state occurs at $B^*$. With further increasing the field
angle from the $c$ axis, the anomaly at $B^*$ slowly shifts to higher fields,
broadens, and becomes smaller in magnitude. Traced up to 30$^\circ$ from the
$c$ axis, it is no longer observed at 40$^\circ$ below 36 T.
