Quantum Sensing exploits quantum resources of well-controlled quantum systems to measure small signals with high sensitivity, and has great potential for both fundamental science and concrete applications. Interacting quantum systems have attracted growing interest in the field of precision measurement, owing to their potential to generate quantum-correlated states and to exhibit rich many-body dynamics. These features provide a novel avenue for exploiting quantum resources in sensing applications. While previous studies have demonstrated enhanced sensitivity using such systems, they have primarily focused on measuring a single physical quantity. The challenge of realizing simultaneous, high-precision measurements of multiple physical parameters using interacting quantum systems remains largely unexplored in experiments. In this study, we demonstrate a first realisation of interaction-based multiparameter sensing with the use of strongly interacting nuclear spins under ultra-low magnetic field conditions. We find that, as the interaction strength among nuclear spins becomes significantly larger than their Larmor frequencies, a different regime emerges where the strongly interacting spins can be simultaneously sensitive to all components of a multidimensional field, such as a three-dimensional magnetic field. Moreover, we observe that the strong interactions between nuclear spins can increase their quantum coherence times as long as several seconds, leading to enhanced measurement precision. Our sensor successfully achieves precision measurement of three-dimensional vector magnetic fields with a field sensitivity reaching the order of 10^–11 T and an angular resolution as high as 0.2 rad. Crucially, this approach eliminates the need for external reference fields, thereby avoiding calibration errors and technical noise commonly encountered in traditional magnetometry. Experimental optimization further boosts the sensitivity of the interacting spin-based sensor by up to five orders of magnitude compared to non-interacting or classical schemes. These results demonstrate the significant potential of interacting spin systems as a powerful platform for high-precision, multi-parameter quantum sensing. The techniques developed here pave the way for a new generation of quantum sensors that leverage intrinsic spin interactions to surpass conventional sensitivity limits, offering a promising route toward ultra-sensitive, calibration-free magnetometry in complex environments.