  We study interacting ultracold atoms in a three-dimensional (3D) harmonic
trap with spin-selective dissipations, which can be effectively described by
non-Hermitian parity-time ($\mathcal{PT}$) symmetric Hamiltonians. By solving
the non-Hermitian two-body problem of spin-1/2 (spin-1) bosons in a 3D harmonic
trap exactly, we find that the system can exhibit third-order (fifth-order)
exceptional point (EP) with ultra-sensitive cube-root (fifth-root) spectral
response due to interaction anisotropies in spin channels. We also present the
general principle for the creation of high-order EPs and their spectral
sensitivities with arbitrary particle number $N$ and arbitrary spin $s$.
Generally, with spin-independent interactions, the EP order of bosons can be as
high as $2Ns+1$, and the spectral response around EP can be as sensitive as
$\sim \epsilon^{1/(2ks+1)}$ under a $k$-body interaction anisotropy. Moreover,
we propose to detect the ultra-sensitive spectral response through the
probability dynamics of certain state. These results suggest a convenient route
towards more powerful sensor devices in spinor cold atomic systems.
