We report $^{115}$In nuclear-quadrupole-resonance (NQR) measurements of the pressure($P$)-induced superconductor CeRhIn$_5$ in the antiferromagnetic (AF) and superconducting (SC) states. In the AF region, the internal field $H_{int}$ at the In site is substantially reduced from $H_{int}=1.75$ kOe at P=0 to 0.39 kOe at $P=1.23$ GPa, while the Neel temperature slightly changes with increasing $P$. This suggests that either the size in the ordered moment $M_{Q}(P)$ or the angle $theta (P)$ between the direction of $M_{Q}(P)$ and the tetragonal $c$ axis is extrapolated to zero at $P^*=1.6 pm 0.1$ GPa at which a bulk SC transition is no longer emergent. In the SC state at $P=2.1$ GPa, the nuclear spin-lattice relaxation rate $^{115}(1/T_1)$ has revealed a $T^3$ dependence without the coherence peak just below $T_c$, giving evidence for the unconventional superconductivity. The dimensionality of the magnetic flutuations in the normal state are also discussed.
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