  Accurate chemical compositions of star-forming regions are a critical
diagnostic tool to characterize the star formation history and gas flows which
regulate galaxy formation. However, the abundance discrepancy factor (ADF)
between measurements from the "direct" optical electron temperature ($T_e$)
method and from the recombination lines (RL) represents $\sim0.2$ dex
systematic uncertainty in oxygen abundance. The degree of uncertainty for other
elements is unknown. We conduct a comprehensive analysis of O$^{++}$ and N$^+$
ion abundances using optical and far-infrared spectra of a star-forming region
within the nearby dwarf galaxy Haro 3, which exhibits a typical ADF. Assuming
homogeneous conditions, the far-IR emission indicates an O abundance which is
higher than the $T_e$ method and consistent with the RL value, as would be
expected from temperature fluctuations, whereas the N abundance is too large to
be explained by temperature fluctuations. Instead a component of highly
obscured gas is likely required to explain the high far-IR to optical flux
ratios. Accounting for this obscured component reduces both the IR-based
metallicities and the inferred magnitude of temperature fluctuations, such that
they cannot fully explain the ADF in Haro 3. Additionally, we find potential
issues when predicting the RL fluxes from current atomic data. Our findings
underscore the critical importance of resolving the cause of abundance
discrepancies and understanding the biases between different metallicity
methods. This work represents a promising methodology, and we identify further
approaches to address the current dominant uncertainties.
